Differential equation Definition and 1000 Threads

Homework Statement Find the general solution f(t) of the differential equation: f''(t) − f'(t) − 12f(t) = 36π . How many free parameters enter the solution, and why? Homework Equations f = fH + fP where fH is the homogeneous solution and fP is the particular solution. The Attempt at a...

Hello guys, I found this forum using google because I need help with simulating bungee jump model. I've already done that with zero initial values and it looks good but I want it more realistic : Let's say L is the length of rope so elasticity force starts acting when y=L so logically time...

Homework Statement Solve the differential equation: dy/dx = 2/(x+e^y) Homework EquationsThe Attempt at a Solution I tried to use the substitution v=x+e^y, but I didn't get very far: v’=1+e^y y’ v’-1=(v-x)y' y’ = (v’-1)/(v-x) (v’-1)/(v-x) (x+v-x)=2 V (v’-1)/(v-x)=2 vv’-v=2(v-x) vv’-3v=-2x...

Basically, I am confused by one question in a practice paper in which the equation is given as follows: dy/dx = e^-2y and I know the general solution is equal to : y = -0.5e^-2y + C which would make sense if it was direct integration however it seems to me it is in fact separable...

Can you advice the changes in this diff equation: $\d{y}{x}=\dfrac{y}{x^2+y^2}$

Homework Statement I need to solve the follwing differential equation $$(\frac{df}{dt}) \dfrac{4 n e^{4nf(t)}-9n e^{2nf(t)} (\frac{df}{dt})^2 + e^{2nf(t)} r^2 \frac{d^2f}{dt^2}+5n (\frac{df}{dt})^4 r^4 - r^4 \frac{d^2f}{dt^2} (\frac{df}{dt})^2}{-e^{2nf(t)}+ (\frac{df}{dt})^2 r^2}=0 $$...

Homework Statement ##\displaystyle (x+3)\frac{dy}{dx} = y - 2##, where x is not 3 and y is not 2. Homework EquationsThe Attempt at a Solution ##\displaystyle (x+3)\frac{dy}{dx} = y - 2## ##\displaystyle \frac{dy}{y-2} = \frac{dx}{x+3}## ##\displaystyle \int \frac{dy}{y-2} = \int...

help to solve the differential equation у*у$^{\prime\prime}$=2х*((у$^{\prime})$^2)

Hi, so I am just starting to learn differential equations and we were told that you have to put the equation into this form. In one of the examples in my lecture notes, which says "Solve (x^2-9)dy/dx+xy=0, x>3" He then says we need to rearrange this into the form given above, so he does this...

Hey guys, I'm going to be honest and say I'm so stuck on this assignment - I really need help! I've took on a third year computational physics course last year - turn your weaknesses into strengths someone told me. Well, I failed and I'm back doing it again this year! So, I just have to pass...

i am given an equation which i have to solve in simulink. the equation is quite veered to me. some one help me in understanding what kind of equation it is so that i can solve it in MATLAB simulink. (2+x^2)theta'' + (2xx' +1)theta' + 9.8(xcostheta-sinthetha)-x''=T

Homework Statement We are given the following differential equation: $$ y+yy'-xy'=0 $$ Let's find the solution. Homework EquationsThe Attempt at a Solution So in my course usually we have to do some sort of substitution by the lines of x/y=z or y/x=z. This equation has proven...

So I have to solve an initial value problem involving the Laplace Transformation method. I have all the terms in Y(t) besides one term, I cannot figure how to change it from frequency domain back into time domain.Not sure how to type in Latex, so i uploaded a picture, using the whiteboard...

An exercise in my text requires me to (in MATLAB) generate a numeric solution to a given second order differential equation in three different ways using a forwards, centered and backwards difference matrix. I got reasonable answers for \vec{u} that agreed with each other (approximately) for the...

<<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...

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...

Hello all, my question is if i should or not be worried about the apparent "missing" (or alternative) content about my DE course. My DE course (and the only one in the list of courses i must take to get my degree) consisted on First order ODEs (Separation of variables, homogeneous, Bernoulli's...

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...

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...

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) =...

dx/dt = x-y^2 dy/dt= x^2 -xy -2x For each critical point, find the approximate linear OD system that is valid in a small neighborhood of it. I found the critical points which are (0,0),(4,2),(4,-2) but have no idea how to do the above question! please help!

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...

[ 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...

We were looking at some examples of systems of differential equations in class a couple days ago, and some of them were simple looking systems. One such was ##\frac{dr}{dt} = 4j## ##\frac{dj}{dt} = r## Why is it that we can't treat this as a scenario where both sides of each equation could...

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...

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...

Let u be density of something (heat, smell, etc.). Assume the something only diffuses; there’s no convection or ballistic transport. Let’s work in one spatial dimension (x). Then u satisfies the diffusion equation, ∂u/∂t = D ((∂^2)u/(dx^2))

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 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 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...

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...

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

$y(x^3e^{xy}-y) \, dx+x(xy+x^3e^{xy}) \, dy=0$ change it into exact differential and help me in solving it

1. Homework Statement It's to do with mirages, but I don't think the physics context is too important. It's also possible that the solution doesn't involve differential equations, and my method is completely wrong. I've been given that: ##A = \frac{n(1+ay)}{ sqrt(1+(y')^2)}## where y' is...

Homework Statement Hi, basically I have a boundary value problem and just want to check that my general solution is correct. x'''' + 16x = 0 Homework EquationsThe Attempt at a Solution I'm pretty sure you make a characteristic equation which would be m4 + 16 = 0. Solving this I get m to be...

Hi evry body i would like to have an help to resolve this exercice below the followin differential equation with its initial condition dy/dt=-lambda t y(t) t>=0 avec y(0)=y0 where lambda is damping coeficient strictly positive. -find the solution of this equation with Euler's explicite and...

Homework Statement Given X'' + iG^2 X + w^2 X = 0 G^2 = h/m w^2= k/m What would be a good "educated guess" to solve that differential equation? My oscillations and waves teacher asked this on a test and since I didn't see anything depending on the speed of the object X assumed it was a really...