Differential equation Definition and 1000 Threads

Solve: $$\sin\left({x}\right)y''+(y'^2-\sin^2\left({x}\right))^{1/2}y'^2-\cos\left({x}\right)y'=0$$ Initial conditions: $y(0)=0$ $y'(0)=1$ Keep in mind that this question was on a Calc I exam worth 5 marks, so please nothing crazy like reduction of order or anything...:D

Salve, Can anybody recommend a book which has lots of differential practice problems?Or a similar book for Laplace transforms? No explanations just the answers and the problems,simply for practicing. Thanks for any help.

Homework Statement ##M\ddot{y} + k_{eq}y = me\omega^2\sin(\omega t)## What is ##m##? Homework EquationsThe Attempt at a Solution In the ODE above, ##M## is the total mass of the problem, correct? For instance, if we had a cantilever beam, ##M = m_b + m_m(0.23)## where ##m_b## is the mass of...

Homework Statement Consider the initial value problem for the system of first-order differential equations y_1' = -2y_2+1, y_1(0)=2 y_2' = -8y_1+2, y_2(0)=-1 If the matrix [ 0 -2 -8 0 ] has eigenvalues and eigenvectors L_1= -4 V_1= [ 1...

Homework Statement y''-y=t-4e^(-t)Homework Equations method of undetermined coefficients The Attempt at a Solution solving for characteristic equation first y''-y=0 r^2-1=0 c_1e^(-t)+c_2e^(t) RHS particular solution t-4e^(-t) y_p(t)= At+B+Ce^(-t) y_pt'(t)=A-Ce^(-t) y_p''(t)=Ce^(-t)...

Homework Statement I have a PDE and I need to solve it in spherical domain: $$\frac{\partial F(r,t)}{\partial t}=\alpha \frac{1}{r^2} \frac{\partial}{\partial r} r^2 \frac{\partial F(r,t)}{\partial r} +g(r,t) $$ I have BC's: $$ \frac{\partial F}{\partial dr} = 0, r =0$$ $$ \frac{\partial...

Homework Statement I do not know how to find f(t) with the given Ampliture 40 and a=pi Homework EquationsThe Attempt at a Solution I have the solution above. my set up was 1/2y''+y'+5=f(t) 1/2S^2* Y(s) + Y(s)+5=f(t)

Homework Statement We are just starting to learn about basic differential equations in Calc 2 and I learned about separable differential equations but I'm not familiar with this style, here's the question: Given the differential equation of the form ay"+by'+y=0, find constants a and b so that...

Homework Statement When an object is submersed in a liquid, it experiences a buoyant force equal to the weight of the liquid displaced by the object. As an object moves through a liquid, there is a resistive force which is directly proportional to the density of the liquid, the cross sectional...

Any help is appreciated 1.)----Find the Character equation for the diff equation d^2y/dx^2-4dy/dx+3y=0 with initial conditions y(0)=0 and y'(0)=12 find the solution y(t) (this is what I have gotten so far on this part) p^2+4p+3=0 then (p-1)(p-3)=0 so p1=1 and p2=3? not really sure...

Homework Statement Find two power series solutions of the differential equation about the ordinary point x = 0. Homework Equations y'' + x^2y' +xy = 0 The Attempt at a Solution Check attachment. I found my y1 and y2, the boxed in answers are the ones the book says are the answers. Can...

Hi, I need suggestions for picking up some standard textbooks for the following set of topics as given below: Ordinary and singular points of linear differential equations Series solutions of linear homogenous differential equations about ordinary and regular singular points...

Homework Statement I used Lagrange to solve a problem and ended up with two differential equationsHomework Equations m_2x''+(k-m_2 {\theta '}^2)x=k(L_o+L_2/2)+m_2 g cos{\theta} and (I_1 +1_2 +m_2 x^2) {\theta}'' +2m_2 \cdot x \cdot x' \theta ' +(m_1 L_1/2 +m_2 x)g sin\theta =0The Attempt at...

Homework Statement A rocket through interstellar dust, no gravity. Solve for v with respect to mass. k is a constant. Drag = -bv Homework Equations [/B] The Attempt at a Solution To start: It should become a separable differential equation, but I am having a lot of trouble solving it...

Amazed by the closeness of equations for orbital angular momentum L and spin angular momentum S, I can't help asking is associated Legendre differential equation involved in solving spin function? I only heard that spin naturally comes from treatment of quantum mechanics with relativity theory...

Homework Statement If y=y(t) is the solution of the initial value problem { y'+(2t+1)y=2cos(t) y(0)=2 then y''(0)=? it is a multiple choice practice problem with choices y''(0)=2 y''(0)=-2 y''(0)=4 y''(0)=0 y''(0)=-4Homework EquationsThe Attempt at a Solution Im really not sure how to go...

Homework Statement Find the general solution: y'-3y=(y^2) Homework EquationsThe Attempt at a Solution divide both sides by y^2 y'(y^-2) -3(y^-1) = 1 we know v=y^(n-1) v=y^-1 v'=d/dx(y^-1) v'=-(y^-2) y' plug it back into y'(y^-2) -3(y^-1) = 1 -v'-3v=1 this is where I think I am making a...

Can you prove a differential equation has no analytical solution? Teach me ,please! Thank you a lot!

I want to solve a differential equation of the form d/dt (R) = B(t) where R and B are two complex matrices, with time dependent functions as their coefficients. I want to solve these 3x3 differential equations (ones on the diagonal are actually coupled) and to obtain a matrix form for R. So...

Homework Statement In the limit as t→∞, the solution approaches x(t) =K \sin[ω(t − t_0)] where K and t0 depend on ω. A>0 and ω≥0. Show that K(ω) = \frac{A}{\sqrt{ω^4 + 2ω^2 + 1}} . Homework Equations Here is the differential equation...

Homework Statement (\partial_t - A\nabla^2 + B)f(x) = \eta(x, t) So I have a homogeneous linear differential equation except for an added noise term ##\eta(t) ##. The noise is uncorrelated between times and has a Gaussian distribution with zero mean. That is we have Gaussian white noise...

So I'm currently taking electricity and magnetism and I'm expected to know how to perform a separation of variables on laplace equation in 2 dimensions.I have taken Zero differntial equations courses and I literally have no freaking idea what's going on. The book I use doesn't spend any time...

Homework Statement In the circuit in the following figure, the resistor is adjusted for critical damping. The initial capacitor voltage is 15 V, and the initial inductor current is 6 mA and R=1250 ohms Find vC(t) for t≥0. Express your answer in terms of t, where t is in milliseconds...

Hi. How can i solve below equation with ndsolver ? dp/dt = a * d^2p/dx^2 * cos^2 (theta) + b d^2p/dt^2 + c d^2p /d(theta)^2 where a , b, c are constant. d^2p/dx^2 is second derivative with respect to x. theta is angle.

Homework Statement This is actually an electromagnetism problem but all the physics is done, I just don't remember how to solve the PDE: \frac{d^2V}{dr^2}=-\frac{2}{r}\frac{dV}{dr} The d's should be del's, just don't know how to do that... Homework Equations Not sure. The Attempt at a...

In the attachment I have used the derivation of the wave equation with a slight modification to derive the diff equation that when solved gives the time independent schrødinger equation. Since I have dome this myself I am worried that this might be totally wrong or a bit wrong. Could someone...

I am would like to solve this differential equation: Where http://ieeexplore.ieee.org.ezproxy.uniandes.edu.co:8080/ielx5/8/6493417/6409989/html/img/6409989-eqdisp-3-small.png Could you give me some practical ideas about the required software and methodology? Thank you very much

Homework Statement Find the differential equation that Q(t) satisfies. 2. Relevent equations Kirchoffs loop law and voltage across a capacitor, resistor and inductor. The Attempt at a Solution [/B] So I'm thinking, by Kirchoffs voltage rule, that the sum of the voltages in this circuit...

Homework Statement The problem is Solve the following differential equation: dy/dx = 6*x*y/(3-x^2) Homework Equations Okay so I know the first step is integrating both sides and separating the variables The Attempt at a Solution So separating the variables and integrating I get integral of...

Homework Statement y'' + 4y' + 4y = 0 ---- y(0) = 1, y'(0) = 5 Find the exact solution of the differential equation. Use the exact solution and Euler's Method to compute Euler's Approximation for time t = 0 to t = 5 using a step h=0.05. Plot Euler's & Exact vs. t and plot Error vs. t. Then...

Homework Statement 2y * y'(t) = 3t^2 such that y(0) = 9 Homework Equations g(y)y'(t) = h(t) The Attempt at a Solution So I have done many of these seperable ones in homework that did not require a parameter so now I got lost. This is what I did;[/B] Integral of 2y dy = integral of 3t^2...

A ball of mass 'm' is inside of a tube that rotates in a horizontal plane around the vertical axis (Drawing a circunference). Attached to the ball (inside of the tube) there is a massless, inextensible rope that goes to the midpoint of the circle described by the rotating tube. The other end of...

So, I should prove that: - \frac{\partial H}{\partial q_i} = \dot{p_i} And it is shown that: - \frac{\partial H}{\partial q_i} = - p_j \frac{\partial \dot{q_j}}{\partial q_i} + \frac{\partial \dot{q_j}}{\partial q_i} \frac{\partial L}{\partial \dot{q_j}} + \frac{\partial L}{\partial q_i} =...

Is the derivative of a function a differential equation? I guess it would be because it involves a derivative, right? Would the solution to the equation just be the original function? Is solving a differential equation just another way of integrating? Like with finding solutions of separable...

from the attached file I get something like the answer as y(x) = e^(e^2x(x/3*(sin(3x)+1/9cos(3x)+c) Im not sure if this is right can you have an answer exponetial of an exponential??

Homework Statement Consider the differential equation y'=x-y^2. Find maxima, minima and critical points; show that for every solution f=f(t) exists T\geq 0 such that f(t)< \sqrt{T}\;\forall t > T Homework Equations The Riccati equation: y'=a(x)y^2+b(x)y+c(x) The Bernoulli equation...

Homework Statement By truncating the differential equation below at n=12, derive the form of the solution, obtaining expressions for all the ancoefficients in terms of the parameter \lambda .Homework Equations The ODE is: \frac{\mathrm{d^2}\phi }{\mathrm{d} x^2} = \frac{\phi^{3/2}}{x^{1/2}}...

Hi, I need help solving this ODE. I know the answer is a Bessel function but I need help on the process of getting there. Initial conditions y(0)=1 and y'(0)=0 xy''+y'+xy=0 I have made it this far... ${x}^{2}*\sum_{n=0}^{inf} [n(n+1)*{C}_{n+2}+(n+1)*{C}_{n+1}+{C}_{n}]*{x}^{n}=0$

Homework Statement Solve the differential equation: \frac{dy}{dx} = x + y Homework Equations Integrating factor equationThe Attempt at a Solution Ok, I am aware that in order to solve this equation, I need to make a substitution: v = x + y However, at this point I am unsure about what to...

How do I go about solving a differential equation of the form \partial_{x}F_{x}(x,y) + \partial_{y}F_{y}(x,y) = g(x,y) Where g(x,y) is a known function and I wish to solve for F. I thought i could apply the method of characteristics but the characteristic equation is dependent on coefficients...

Hi, I need help solving this ode, when I try to solve it I end up with a big crazy answer and I believe it should be simpler. (dy/dx)^2=((ay^4)/2)-(a+1)y^2+1 y(0)=0, y'(0)=1 and a is within [0,1]

Solve the 2nd order nonlinear differential equation, with initial conditions y(0)=0 and y'(0)=1 y''=2ay^3-(a+1)y with a within [0,1] I am pretty much lost on how to go about solving this. It would be greatly appreciated if someone could point me in the right direction on this. Thanks!

In class we discussed RLC circuits in series. My homework problem, however, has me analyzing an RLC circuit in series. a) Write the differential equation that describes the voltage with respect to time. b) Find the natural frequency of oscillation and the damping constant of the circuit...

Homework Statement Mass , r, of a round object grows in proportions with its SA. The density of the object is constant. Find the differential equation for the change in 'r' of the object over time. Arbitrary constants can be combined but final answer must depend on only r and constants...

For each epsilon greater than 0, show that the differential equation x'=x^2-1-cos(t)-epsilon has at least one periodic solution with 0 less than x(t) less than or equal to (2+epsilon)^1/2

Homework Statement I want to solve number 13. I have my work on the attached file. Homework Equations The Attempt at a Solution I've tried to solve the system by elimination and substitution. I keep failing again and again

Homework Statement y'sin(2t) = 2(y+cos(t)) y(\frac{∏}{4}) = 0 Homework Equations \frac{dy}{dx} + p(x)y = q(x) y = \frac{\int u(x) q(x) dx + C}{u(x)} where u(x) = exp(\int p(x)dx) The Attempt at a Solution I've set the equation in the form above, simplified the RHS and solved for...

Hi everyone, I need some help to solve this differential equation. The question states "Use the perturbation or multiple scale method to find the third-order approximate solution for the following system: diff(x(t), t, t)+w^2*x(t)*(1+epsilon*x(t)^2) = 0 " Currently, I am still...

Hello. I need some help solving a differential equation. I think where I'm going wrong is integrating one side via partial fractions, but I'm not quite sure where my mistake is. Using Wolfram, I found the correct answer, which is below. Thanks. Homework Statement Solve the following initial...

Hi all , I would like to solve the following partial differential equation. (∂α/∂t)=G[sub(α)] *(a'-a) I attached the equation and solution here as an image. I don't know how it was derived. I hope someone can help me