Differential Definition and 1000 Threads

I need a good book on differential equations.

Hey! :o When we have a system of differential equations $$\bigwedge_{j=1}^n L_j y=f_j$$ is it possible that we reduce it into one differential equation $Ly=f$ so that the system has a solution iff the differential equation $Ly=f$ has a solution? (Wondering)

Hello to all, I am a new member, but I've been reading and getting help from this forum for a year! I recently started to study about stochastic calculus because I am considering risk management/ actuarial/ finance job. I would appreciate your help. If we have Poisson $(\lambda)$ and $W$...

If I am going to change my truck differential and find some suitable one for it, What could be the possible effects on vehicle performance of that differential..?? For now I haven't plan for it. Just want to know the basic Idea of what could be affected.

<<Moderator note: Missing template due to move from other forum.>> Good afternoon. I'm trying to solve a differential equation with bessel function solutions. I am trying to solve \begin{equation*} y''(x)+e^{2x}y(x)=0 \end{equation*} using the substitution ##z=e^x##. The textbook this problem...

Homework Statement For each Set write the differential equation they are a solution to. It is also asked to find the wronskian but I remember how to do that. (I am doing this on my own to brush up before I have to take mathphys next semester) 1. e-x,e-4x 2, 1,x,x2 Homework EquationsThe Attempt...

Is my background enough to learn partial differential equations? I have completed up to calculus 2 and linear algebra. I am currently taking Cal 3 and Ordinary Differential Equations. I am doing well in both courses. I would like to learn PDE and a bit more Linear Algebra, during the winter...

Hello, So i know that the gravitational acceleration experienced by a body is -GM/||d||^2 * dhat, where dhat is the current displacement unit vector, which has a magnitude of 1. the magnitude of a vector is equal to to the square root of the sum of its squared components. This will be a 2d...

Hi , while trying to prove gauss law for electric field from gauss theorem i came up with this problem . as Gauss' differential law expresses ∇⋅E = ρ/εο what i get from that is ... the divergence of electric field which is the flux density is related to the charge density ...but i can't get...

Hi there. I've been struggling with this problem for days now (4 days, no joke) and I feel like I have a mental block and really cannot get any further. I have a system that's described by f(t) = g''(t) + 15g'(t) + 1600g(t) Where the input is g(t) The problem is to, with this information...

Chasing a ghost perhaps but in the process of pressure testing a simple propane furnace installation I installed a water Column pressure gauge. Over a period of 11 hours the pressure gauge reading will go from 10" WC to 0" WC. In the course of trying to understand this I installed a manometer...

Good evening I have these coupled equations and was wondering if there is any chance solving them analytically. If not, how would you approach it numerically? (shown in attachment) Thank you very much

I'm trying to deduce the differential equation for temperature for a triangular fin: I know that for a rectangular fin, such as: I can do: Energy entering the left: q_x= -kA\frac{dT(x)}{dx} Energy leaving the right: q_{x+dx} = -kA\frac{dT(x)}{dx} - kA\frac{d² T(x)}{dx²}dx Energy lost by...

I have this basic differential equation du/dt=(u^2)*(sin t) This is obviously a separable diff eq. So what I've done is: g(t) = sin t h(u) = u^2 1/(u^2) du = sin t dt Integrating both side... 1/y = - cos t + c therefor y = - 1/(cos t + c)Which is wrong, there isn't supposed...

Homework Statement I'm stuck on Question #2 part A/B Homework Equations y'=r(1-y/k)y-h=y^2-ky+kh/r y''=2y-k Roots for y'= (k+/-sqrt(k^2-4kh/r))/2 I am assuming the positive root is y2 h<rk/4 [/B] The Attempt at a Solution on part a I'm getting the roots to be y2=(K+sqrt(k^2-4kh/r))/2 and...

Hey, I am struggling to understand what the following is in terms of the mathematics (see Nakahara page 193 at the bottom...

Homework Statement Consider the boundary value problem \begin{equation} u''(t)=-4u+3sin(t),u(0)=1,u(2)=2sin(4)+sin(2)+cos(4) \end{equation} Homework Equations Derive the linear system that arise when discretizating this problem using \begin{equation} u''(t)=\frac{u(t-h)-2u(t)+u(t+h)}{h^2}...

I can not find a solid explanation on this anywhere, so forgive me if this has been addressed already. Given something like y''+y'-(x^2)y=1 or y''+2xy'-y=x, how do I approach solving a differential with a power series solution when the differential does not equal zero? Would I solve the left...

Hello 1. Homework Statement We define the Dupin indicatrix to be the conic in TPM defined by the equation IIP(v)=1 If P is a hyperbolic point show: a. That he Dupin indicatrix is a hyperbola b/ That the asymptotes of the Dupin indicatrix are given by IIP(v)=1 , i.e., the set of asymptotic...

Homework Statement Hi,I am learning to solve 2nd-order differential eq. Suppose I have a equation dy/dx - 3x = 0...(1) Then dy/dx = 3x -----> x = 3(x^2)/2 Now if I have a 2nd order ODE such that: d^2y/dx^2 = 3....(2) Then it could be solved by integrating both sides wrt x twice,which yields y...

Homework Statement Y''-((Y')^2)+(C1*exp(Y))=C2 C1 and C2 are constants. exp = e Homework Equations No clue how to start this The Attempt at a Solution Y'=A=dY/dt Y=At+C3 (not sure) A'-(A^2)+C1exp(At+C3)-C2=0 A'-(A^2)+C1exp(C3)exp(At)=0 let C=C1*exp(C3) A'-(A^2)+Cexp(At)=0

I'm writing a paper about the projectile motion with the consideration og air resistance - I have obtained two formulas: ax = k*(vx2+vy2)0.5 * vx ay = k*(vx2+vy2)0.5 * vy - g (K and g are constants; K = -0,02, g =9,82) I cand write these two as 2 different differential equations: v'x(t) =...

Differential equation: F(y'',y',y,x)=0, y=y(x). Now, there is g=g(x) with F(g'',g',g,x)=δ, where δ is small. Then, can g(x) be taken as an approximate solution of F(y'',y',y,x)=0?

Hello, I'm struggling with a simple problem here. It asks me to solve the following initial value problem: So far I've calculated the integration factor μ(x) = ex-x2 and I multiplied both sides of the equation by it and got this...

Homework Statement Text from a classical mechanics textbook ( uploaded picture ) shows 2 diff equation describing the motion graphically presented in the uploaded picture. How were these set up? Homework EquationsThe Attempt at a Solution I don't have a slightest clue as how are these...

[ NOTE ] Thread moved to homework forums by mentor suppose in a dark room a candle is burning, so darkness increases as we move away from the candle. from the below diagram can anyone derive a differential example to show the rate of change of darkness from candle to point B. supposing...

Hey! :o Each element of the ring $\mathbb{C}[z, e^{\lambda z} \mid \lambda \in \mathbb{C}]$ is of the form $\displaystyle{\sum_{k=1}^n α_kz^{d_k}e^{β_kz}}$. A differential equation in this ring is of the form $$Ly = \sum_{k=0}^m \alpha_k y^{(k)}(z)=\sum_{l=1}^n C_lz^{d_l} e^{\beta_l z} , \ \...

Homework Statement OK, this differential equation was technically created by me, because i need to clear my doubts. Y'' + sqrt(X)*Y' + X^3*Y=3sin(x) and actually just any initial conditions as long as the solution is something i can understand, let me expand my doubt further. I've never solved...

Hey! :o I want to check if a linear differential equation of second order has a solution in the ring $\text{Exp}(\mathbb{C})$. We define $\text{Exp}(\mathbb{C})$ as the set of expresions $$\alpha=\alpha_1 e^{\mu_i x}+\dots \alpha_N e^{\mu_N x}$$ where $\alpha_i \in \mathbb{C}$ and $\mu_i \in...

Hey! :o When we have the non-homogeneous differential equation $$ay''(x)+by'(x)+cy(x)=f(x)$$ and the non-homogeneous term $f(x)$ is of the form $e^{mx}P_n(x)$ we know that the particular solution is $$y_p=x^k(A_0+A_1x+ \dots +A_nx^n)e^{mx}$$ where $k$ is the multiplicity of the eigenvalue...

\begin{array}{l} u = u(x,y) \\ v = v(x,y) \\ and\\ {u_x} + 4{v_y} = 0 \\ {v_x} + 9{u_y} = 0 \\ with\ the\ initial\ conditions \\ u(x,0) = 2x _(3)\\ v(x,0) = 3x _(4)\\ \end{array} Easy, u_{xx}-36u_{yy}=0 and v_{xx}-36v_{yy}=0 General solution u\left ( x,y \right )=h\left ( x+6y \right...

Homework Statement I've attached an image of the problem question, it's Q1 I'm working on This is what I have so far: we have two components of SHM, position x and velocity v. when x = 0, v = a maximum, when v = 0, x = a maximum this is represented by sin & cos functions. where x =...

#17 If you can't see the picture: Suppose that y1, y2, and y3 are solutions to a third order constant coefficient homogeneous differential equation. Suppose further that for all real t, W(y1,y2)(t)>0, but also W(y1,y2,y3)(0)=0. Then there exists c1 and c2 such that c1y1(t) + c2y2(t) =y3(t) for...

Hey! :o I want to check if there is a solution of a linear differential equation of first order in the ring of exponential sums $\text{EXP}(\mathbb{C})$. I have done the following: The general linear differential equation of first order is $$ax'(z)+bx(z)=y(z) \tag{*}$$ where $x,y \in...

Homework Statement This is a interesting (morbid) problem from Simmons- Calculus with Analytic Geometry. In a certain barbourous land, two neighbouring tribes have hated one another from time immemorial. Being barbourous peoples, their powers of belief are strong, and a solemn curse pronounced...

Homework Statement After a mass weighing 8 pounds is attached to a 5-foot spring, the spring measures 6.6 feet. The entire system is placed in a medium that offers a damping constant of one. Find the equation of motion if the mass is initially released from a point 6 inches below the...

There are two courses I can take for a Differential Equations class at my school. One is for Engineering students and is described this way (I'm a physics major fyi): This course presents an introduction to the theory of differential equations from an applied perspective. Topics include linear...

Homework Statement A circuit consists of a voltage source, voltage ##V## , a resistor, resistance ##R##, and a capacitor, capacitance ##C##, in series. (i) Show that the charge ##Q(t)## in the capacitor satisfies the equation ##R Q' (t) + Q(t)/C = V ##. (ii) Suppose that ##R##, ##C## and...

Homework Statement We have the equation ## (\frac{dr}{ds})^2+(\frac{l}{r})^2=1 ## and want to solve to get ## r=\sqrt{l^2+(s-s_0)^2}## Homework EquationsThe Attempt at a Solution I have worked backwards, plugging in the solution to prove that it is correct, but the closest I have gotten to...

Homework Statement A uniform 10-foot-long heavy rope is coiled loosely on the ground. One end of the rope is pulled vertically upward by means of a constant force of 5lb. The rope weighs 1lb/ft. Use Newton's second law to determine a differential equation for the height x(t) of the end above...

Homework Statement Chemical reactions being studied in which a body A undergoes transformations according to the following scheme: http://prntscr.com/8shuvb k1, k2, k3 , k4 are the rate constants . We denote x (t ), y ( t) , z (t) the respective concentrations of the products A, B, C at a...

Homework Statement Water with a small salt content (5 lb in 1000 gal) is flowing into a very salty lake at the rate of 4 · 105 gal per hr. The salty water is flowing out at the rate of 105 gal per hr. If at some time (say t = 0) the volume of the lake is 109 gal, and its salt content is 107...

Hey guys, I have a question concerning the rewriting of a differential equation solution. In the example above, they rewrite [y=(plus/minus)e^c*sqrt(x^2+4)] as [y=C*sqrt(x^2+4)]. I understand that the general solution we get as a result represents all the possible functions, but if we were to...

Hi, I am struggling to find the solution to the following equation. I can't account for the exponential term, so clearly something is going wrong... 1. Homework Statement Find the general solution to ##x' = tx + 6te^{-t^2}## where ##x(t)##. Homework EquationsThe Attempt at a Solution [/B]...

Hey! :o I want to check if we can always find a solution of a linear differential equation of first order in the polynomial ring $F[z]$. I have done the following: The general linear differential equation of first order is $$ax'(z)+bx(z)=y(z)$$ where $x,y \in F[z]$. Or is it possible that...

Homework Statement So there is a falling object, you have to take into account the boyant force, the pull of gravity and the drag force A time dependent distance equation is what we're looking for Homework Equations Fd=CdApav2/2 Where Fd is the drag force Cd is the drag coefficient A is the...

Homework Statement I am reading a note on differential equation.There is a point that I don't understand,hopefully someone can explain (Please see the attched) Homework EquationsThe Attempt at a Solution The notes wrote " a1t + b1 x + c1 = a1T + b1X a2t + b2t + c2...

Let the PDE $u_{xx}-4u_{xy}+4u_{yy}=0.$ Reduce to the canonical form.Good Morning MHB :). My problem is find the canonical form of the PDE know an variable change. But how I can transform the equation? Thanks.

Please help me solve this differential equation for the initial condition (0,-1): dx/dy = ((1+x^2)^(1/2))/(xy^3) I think I'm doing something wrong because I end up with ((x^2)(y^3))/2 = ((x^2)+y)^(1/2) + c, but when plugging in the initial condition it ends up being the square root of...

Homework Statement (4x^3y^3-2xy)dx+(3x^4y^2-x^2)dy=0[/B]Homework Equations (4x^3y^3-2xy)dx+(3x^4y^2-x^2)dy=0 The Attempt at a Solution i expanded it as 4x^3y^3dx-2xydx+3x^4y^2dy-x^2dy=0 next we have to take the common such that there will be m(X)(xdy+ydx)[/B] m(x) is the common onee