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# Ordinary Differential Equations

### Error function - Ordinary Differential Equation

Initial Value Problem. See attached file for full problem description. Express the solution of the initial-value problem y' - 2xy = 1, y(1) = 1, in terms of erf(x).

### Solve an ordinary differential equation

Solve an ordinary differential equation in the attached file.

### Euler Function Chinese Remainder Theorems

(See attached file for full problem description) --- We consider the special case when m=3 and n=5. (a) Find the explicit function from the Chinese Remainder Theorem Chapter summary. (Recall that g is the inverse function of f.) (b) Write down all ordered pairs (a,b) &#1028; . (c) Compute g(a,b) for each ordered pair in

### First order ODE Reduced to homogeneous ODE

Given (t-3y-5) dt + (y-t+1) dy =0 introduce a change of variables to transform this ODE into a homogeneous one and solve.

### Find the steady state solution for ODE

Find the steady state solution for non-homogeneous ODE as found in the attached file.

### Ordinary Differential Equation : Initial Value Problem

Please see the attached file for the fully formatted problem. keywords : ODE IVP

### Solving ordinary differential equation

Solve: (e^(x)+y)dx + (2+x+y*e^(y))dy = 0 , y(0) = 1

### Ordinary Differential Equation : Defined on the Domain

In the solution of the ODE : dy/dx = -y-sinx defined on the domain {x: -pi < x < pi} using 4th order Runge-Kutta I am trying to provide step-by-step detail of the first two steps (h=pi/30).

### Solve the Ordinary Differential Equation : xy'- y=2x^2

Solve the Ordinary Differential Equation 1 ) xy'- y=2x^2

### Homogeneous Equations Intervals

F_1 (x) = 1 + x, f_2 (x) = x, f_3 (x) = x^2 interval (-&#8734;, &#8734;).

### Differential equation solved with variables separable method

Let x: [0, infinity) -> R and y: [0, infinity) -> R be solutions to the system of differential equations: x' = - x y' = - sin y With initial condition: x(0) = y(0) = alpha, where alpha belongs to [0, pi) (a) Show that |x(t)| =< alpha for all t >= 0 (b) Show that | y(t) -

### ODE - Bernoulli Equation

I would like to see a step by step solution using the Bernoulli equation.

### Zeroes of linearly dependent, nontrivial solutions of ODE

Show that the zeros of two linearly dependent, nontrivial solutions of the following equation coincide. y" + A(t) y = 0

### Series Solutions of Second Order Linear Equations

Verify that x0=0 is an ordinary point of the differential equation: y''+ xy' + 2y = 0 Find two linearly independent solutions to the differential equation in the form of a power series about x0=0. If possible, find the general term in each solution. Write the general solution Verify that x0=0 is an ordinary point for the

### Solving an Ordinary Differential Equation

DP/dt = m(a0)[exp(-z1)t] - (z2/z1)P Solve this differential equation with a = ao at t=0 and a=a at t=t to show that: P = [mz1(a)] / [z2 - z12] + [mz1(ao) / (z12- z2)](a/ao)^(z2/z12) Where the last term in this equation is a/ao "raised to the power of" z2/z12 ---

### Solving a Particular solution to an Ordinary Differential equation

See attached problem. PLEASE NOTE!!! I have noted in the problem statement that I have solved the homogeneous portion of the differential equation, and I need assistance in solving for the particular solution and finally the whole solution. I have gotten 2 responses from other OTA's that are as follows: "The point is that y

### Euler's and Rutta methods

Discuss how to choose the step size h.... missing.jpg contains the given differential equation to the question in the other *jpg file.

### Explicit Euler Method

Was Euler the ancient fortune-teller? He almost was. One of his principles, the explicit method says that your future days could be predicted from your present day knowing your past provided your time frame is not too large. Have a look at the solution to a system of non-linear differential equations system using explicit or

### Ordinary Differential Equations and Initial-Value Problems : Unique Solution

Find the unique solution satisfying initial conditions y(1)=0 and y'(1)=1 for ty''-(t+2)y'=2y=0, t not equal to 0 Solve t^2y''+3ty'+5y=0 Solve the initial value problem. y''-2y'+y=2e^t+3 y(0)=4 and y'(0)=3

### Separation of Variables : Separating PDEs into two or three ODEs

Separation of Variables... Please see the attached file for the fully formatted problems.

### Ordinary Differential Equations: Boundary Value

Solve each of the following ODE's for y(x): (a) y" + 16y = 0 with y(0) = 1 and y'(0) = 0. (b) y" + 6y' + 9y = 0 with y(0) = 1 and y'(0) = 0. (c) y"' - y" + y' - y = 0 with y(0) = 1 and y'(0) = y" (0) = 0.

### Ordinary Differential Equation

Ordinary Differential Equation Determine if the following system has nay non-constant solutions that are bounded, i.e. do not run off to infinity in magnitude x' = x(y - 1) y' = y(

Draw the phase portrait for the following system: x' = xy y' = (x^2)y

### Show that this system is a Hamiltonian system.

Please give me a step-by-step solution to this attached ODE. Consider the following system: x' = -2y y' = x/2 a. Show that this system is a Hamiltonian system. b. Us a Hamiltonian to sketch the phase portrait for this system.

### Space Factor, Time Factor, Eigenvalues and Sturm-Liouville

7. Consider the differential equation ut =1/2 uxx + ux for 0 <x < pi, t > 0 with boundary conditions u(0,t) = u(pi,t) = 0. (a) Separate variables and write the ordinary differential equations that the space factor X(x) and the time factor T(t) must satisfy. (b) Show that 0 is not an eigenvalue of the Sturm-Liouville proble

### ODE: Phase Portrait and a Rough Sketch of a Solution

Draw the phase portrait associated with x'' - 2x' + 2x = 0 and draw a rough sketch of the solution x(t) that satisfies x(0) = 1 and x'(0) = 0. See the attached file for the problem.

### Ode - Convert into System of Differential Equations

Convert {see attachment} into a system of differential equations and classify the resulting system.

### Solve the Ordinary Differential Equation

Solve: (1+x)y' = x

### ODE: Variation of Parameters

Please see the attached file for the fully formatted problems. One solution of the equation attached is y(t) = t. Find the general solution. Use variation of parameters to find a particular solution of the equation attached.

### Phase Plane

Solve y" + w^2y = 0 w= the symbol omega subscript zero (0).