Differential equations Definition and 999 Threads

Is this a homogeneous DE? 3y'''' + 21y'' + y' + 6y = 0 So... since a(n-1)y''' is missing, would this still by definition be a homogeneous differential equation?

I have a set of differential equations with the basic form: dy_n/dt = t*(a_(n-1)*y_(n-1)+b(n+1)*y_(n+1)-2c_n*y_n) So the time depence is a simple factor in front of the coefficient matrix. Does this set of differential equations have closed form solutions?

I can't really find much differential equations problems workbook. I really want one but resources are limited. Can you please send amazon links and etc. that I can order a differential equations problems workbook? Also, it would be greatly appreciated that the workbook at least covers topics...

Dear all, I have posted a similar question in another forum and the general consensus seems to suggest that it is not possible to symbolic solve a system of coupled second order different equation with damping (dissipation) and driving forces. However, I have found in many papers and books...

Hello everyone I just want to ask if anyone could help me or at least tell me if it is possible to solve the couple equations using matlab I saw ode45 but that is for one equation only Thank uou

Homework Statement If y1 and y2 are solutions to y"-y = 0 then c1y1+c2y2 represent all solutions to the differential equation for all scalars c1 and c2 Homework Equations The Attempt at a Solution Basically, my TA's solutions to his worksheet said it was true, and I'm not sure if...

Homework Statement hi, i have difficulties in this question... can you teach me how to get the ans please... i don't have the ans . this involved differential equations Homework Equations The Attempt at a Solution

Homework Statement Find the zero input and zero state response for the following system y''(t) + 3y'(t) + 2y(t) = 2 x'(t) - x(t-1) where x(t) = (2e^-t)*u(t) U(t) is the step function Homework Equations Y = Yh + Yp Y = Yzsr + Yzir The Attempt at a Solution I can't find...

For a system of linear differential equations with constant coefficients with known initial conditions an analytical solution can be found. I however have a system of linear differential equations, where the coefficients are timedependent with the dependence of the coefficients being...

-2 ln |20-2h| = kt + c kinda lost. solving (i) would be enough for me

Hi everyone, I'm taking the Differential Equations for the first time, and I want to know the most helpful textbook for the subject. We had the following example: Find the differential equation which its general solution is: y=C_{1}+C_{2} x+x^{2} Solution: y^{'}=0+C x+2x y^{''}=0+0+2...

Hello, PF! As I was reading my P-Chem textbook, I noticed most thermodynamic equations involve partial derivatives, like these ones: C_V = {\left( \frac {\partial E}{\partial T} \right )}_V {\left( \frac {\partial H}{\partial T} \right )}_P = {\left( \frac {\partial E}{\partial T} \right )}_P +...

Simple harmonic motion: ##y'= -z,~z'= f(y)##the modified explicit equation are$$y'=-z+\frac {1}{2} hf(y)$$$$y'=f(y)+\frac {1}{2} hf_y z$$ and deduce that the coresponding approximate solution lie on the family of curves $$2F(y)-hf(y)y+z^2=\textrm{constant}$$where ##f_y= f(y)##. What are the...

Show that the nonlinear oscillator $$y" + f(y) =0$$ is equivalent to the system $$y'= -z $$, $$z'= f(y)$$ and that the solutions of the system lie on the family of curves $$2F(y)+ z^2 = constant $$ where $$F_y= f(y)$$. verify that if $$f(y)=y$$ the curves are circle. => nonlinear oscillator...

Homework Statement a function has the feature that at any point, the product of its gradient and the x-cordinate is equal to the square root of the y-cordinate multiplied by 5. Part A: Write out a differential equation that describes the function Part B: If the curve passes through the point...

Homework Statement consider y'' + 2y' - 3y = 1 + xe^x, find the particular solution The Attempt at a Solution so f(x) = 1 + xe^x f'(x) =e^x + xe^x f''(x) = 2e^x + xe^x so it looks like my particular solution is going to have a constant term, an e^x term and an xe^x term, so I can...

A bit related to my other topic but here goes: I have the set of differential equations: x1' = a-ax1-ax2 x2' = b-bx1-bx2 What is the solution to such a set? I could google systems of differential equations, but that turns up large texts on the theory. I just wonna know in a few lines...

Homework Statement hi, all… can anyone help me with this question? i got stucked here? can you figure out which part contains mistake or post the full solution here? thanks in advance! http://i.imgur.com/RZpquyd.jpg?1 http://imgur.com/RZpquyd&Eoaa0mm#0 Homework Equations The...

I would like to learn this. Can someone teach me? The things like δy2/δ2x and solving for x and y. :rolleyes:

Hi, this question came up in my midterm and I was hoping to know if this is the correct method or answer.

Can someone please help me to calculate the following using separation of variables: dy/dx = x*(1 - y^2)^(1/2) to that the solution is in the form: y =

I have a problem I would like some guidance on. I need to find the values of $k$ for which $x^2+ky^2$ is a Liapunov function for the system $$\dot{x}=-x+y-x^2-y^2+xy^2, \dot{y}=-y+xy-y^2-x^2y$$ **My attempt:** $$\dot{V} = \frac{\partial V}{\partial x} \times \frac{dx}{dt} + \frac{\partial...

1. The problem statement, all variables and given/known This is a group project for differential equations. I ended up without a group, lucky me. I've been trying to work through this on my own but I am stuck. Sorry about the pictures, typing it all out would of taken ages...

AP Physics student here, I'm working on a problem that takes into account air resistance, where something is thrown up at initial velocity v_0, and the drag force is proportional to the velocity, so, \vec{F_{drag}}=-k\vec{v}. Using Newtons second law and making up positive, down negative, you...

Hello Homework Statement Find the general solution of the following differential equations. In each case if y = 2 when x = 1, find y when x = 3. x \frac{dy}{dx} = \frac{1}{y} + y Homework Equations The Attempt at a Solution x \frac{dy}{dx} = \frac{1}{y} + y x ...

Hello, these are the first differential equations I've tried to solve... Homework Statement Find the general solution of the following differential equations. In each case if y = 2 when x = 1 find y when x = 3. 2x \frac{dy}{dx} = 3 Homework Equations The Attempt at a Solution 2x...

Hello all, I am currently having trouble with this Differential Equations problem. Let x = F(t) be the general solution of x'=P(t)x+g(t), and let x=V(t) be some particular solution of the same system. By considering the difference F(t)−V(t), show that F(t)=U(t)+V(t), where U(t) is the general...

Homework Statement Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at the same rate. Determine...

Find the differential equation or system of differential equations *** Find the differential equation or system of differential equations assoicated with the following flows a) ##\phi_t (x) = \frac{x}{\sqrt{1-2x^2t}} ## on ##{\mathbb R} ## b) ##\phi_t (x,y) = (xe^t, \frac{y}{1-y^t}) ## on...

Homework Statement Consider the first order differential equation \frac{dx(t)}{dt} + ax(t) = f(t), x(0) = x_{0}, t\geq0 Suppose the "input signal" f(t)=e^{-t}, t\geq0 . (a) Find the solution to the equation. Find a condition on the parameter a so that the solution of the (forced) system...

Homework Statement Solve the equation dy/dx = x/(y^2√(1+x)) Homework Equations The Attempt at a Solution I separated them: y^2 dy = dx/√(1+x) I then integrated the dy side, I got (1/3)y^3 + C. I am stuck at integrating the dx side. Thanks in advance!

I have to solve the following differential equation (that I found in an article): \frac{1}{r^{5}}\partial_{r}(r^{5}\partial_{r}h(r)) -E\frac{h(r)}{r^{2}} = - \frac{C}{r^{5}}\delta(r-r_{0}) where E and C are two constants. The authors of the article first find a solution of the previous...

Homework Statement Generate an open loop u(t) and simulate. Plot x(t) and y(t) \dot{x} = Vcos(θ) \dot{y} = Vsin(θ) \dot{θ} = u I am given initial values. All are 0 except for \dot{x}(0) = V. Homework Equations Laplace Transform Tables The Attempt at a Solution I think I...

Homework Statement Solve the system ##\dot{x}=-2x+y+5sint## and ##\dot{y}=x-2y+3## for ##x(0)=1## and ##y(0)=1## Homework Equations The Attempt at a Solution Well, I tried expressing x from the second equation, derived it and inserted it in the first equation but this process...

Hi! I would like to ask anyone with some spare time to check my assignment questions. Last time I was asked to post one task at a time so I will. Thank you in advance for your time. Task 6: In a galvanometer the deflection θ satisfies the diffrential equation: d2θ/dt2+2(dθ/dt)+θ=4...

Hi! I would like to ask anyone with some spare time to check my assignment questions. Last time I was asked to post one task at a time so I will. Thank you in advance for your time. Task 5: Find the particular solution of the following differential equations: a) 12(d2y/dx2)-3y=0...

Hi! I would like to ask anyone with some spare time to check my assignment questions. Last time I was asked to post one task at a time so I will. Thank you in advance for your time. Task 3: A capacitor C is charged by applying a steady voltage E through a resistance R. The p.d. between the...

Hi! I would like to ask anyone with some spare time to check my assignment questions. Last time I was asked to post one task at a time so I will. Thank you in advance for your time. Task 2: Determine the equation of the curve which satisfies the differential equation...

Hi! I would like to ask anyone with some spare time to check my assignment questions. Last time I was asked to post one task at a time so I will. Thank you in advance for your time. Task 1: Solve the differential equation: x(dy/dx)+x2=5 given that y=2.5 when x=1 Solution: x(dy/dx)+x2=5...

1. 1.Homework Statement Use power series to evaluate intial value problem y''-xy'-2y=4x^2 y(0)=1 and y'(0)=1 Homework EquationsThe Attempt at a Solution I got the series Cnx^n and took its derivative and plugged it into the formula and I got but when I factor out x^n and set that...

Consider the first order differential equation dy/dt = f(t,y)= -16t^3y^2, with the inital condition y(0)=1. Estimate the lipschitz derivative for the differential equation by substituting the exact solution into ∂f/∂y. =I found the exact solution by using the separable of variable and...

I have not met differential equations involving the composition functions (also not much literature on it). Assume we know the form of g=g(x), and need to solve the following differential equation, finding f=f(x): (g∘f)f'=g Where g∘f=g(f(x)). Does anybody have a strategy for solving...

Homework Statement Hello, I am trying to put the following equations into matrix form in order to solve the system. If anyone could please explain to me how to do it or show me an example it would be awesome. All material given in question: For the system of inhomogeneous differential...

If a_3(x)y'''+a_2(x) y''+a_1(x) y'+a_0(x)y=f(x) is an ODE with particular solution y_{p1} and a_3(x)y'''+a_2(x) y''+a_1(x) y'+a_0(x)y=g(x) is an ODE with particular solution y_{p2}, then the ODE a_3(x)y'''+a_2(x) y''+a_1(x) y'+a_0(x)y=f(x)+g(x) has the particular solution y_{p1}+y_{p2}.

Let A be an 3x3 matrix such that A\mathbf{v_1}=\mathbf{v_1}+\mathbf{v_2}, A\mathbf{v_2}=\mathbf{v_2}+\mathbf{v_3}, A\mathbf{v_3}=\mathbf{v_3} where \mathbf{v_3} \neq \mathbb{0}. Let B=S^{-1}AS where S is another 3x3 matrix. (i) Find the general solution of \dot{\mathbf{x}}=B\mathbf{x}. (ii)...

Homework Statement Find General Solution of the Following System (2D+5)x - (2D+3)y = t (D-2)x + (D+2)y = 0 https://dl.dropboxusercontent.com/u/32294083/Emath/New%20Doc%203_1.jpg Using the Quadratic Formula I get nothing so I am not sure what the complementary solution is...

Homework Statement I am going to copy-paste this text that my friend made (because we both have the same doubt and we don't know to work around it. This is a long post, so warning): "I'm currently unsure of how these two problems work. I've tried working at them in different ways but i don't...

Homework Statement A certain nuclear plant produces radioactive waste in the form of strontium-90 at the constant rate of 500kg. The waste decays exponentially with a half-life of 28 years. How much of this radioactive waste from the nuclear plant will be present after the following...

Homework Statement A homicide victim is found to have a temperature of 31°C at the stroke of midnight. At 1:00AM his temperature dropped to 29°C. Assuming that the temperature of the room stays at 20°C, when did the murder take place? Homework Equations - The Attempt at a Solution...

Homework Statement a. Assume that yo dollars are deposited into an account paying r percent compounded continuously. If withdrawals are at an annual rate of 200t dollars (assume these are continuous), find the amount in the account after T years. b. Consider the special case if r = 10% and...