Question

solve the second order ode ( I have problem to choose right yp for term has cosh or sinh)

y"-6y'+y=6 cosh x

y(0)=0.2

y'(0)=0.05

Answer #1

Problem 8 Let a(t) =/= b(t) be given. The factorization for a
second order ODE is commutative if (D + a(t) I) (D + b(t) I) y = (D
+ b(t) I) (D + a(t) I) y.
• Find condition on a(t) and b(t) so that the factorization is
commutative.
• Find the fundamental set of solutions for a second order ODE
that has a commutative factorization.
• Use the above results to find the fundamental set of solutions
of...

Using Matlab, solve the following ODE using Euler's
method...
I have to perform solve the ODE with both step sizes and plot
both on the same graph.
y'=1/y, Initial Condition y(0)=1. step size = 0.1 and 0.01
The interval is from 0 to 1.
UPDATE: I actually figured it out myself! THANKS

5.1 Application of Linear Second Order ODE): Consider the
‘spring-mass system’ represented by an ODE x′′ (t) + 16x(t) = 5 sin
4t with ICs: x(0) = 2, x′ (0) = 1. Answer the questions
(a)–(c):
(a) Is there damping in the system? Why or why not?
(b) Is there resonance in the system? Why or why not?
(c) Solve the ODE.

In this problem, you will solve the following first order linear
ODE: y' + (1/x)y = (2/x2 )+ 1 with y(1) = 1.
a) Solve the complimentary equation
b) Use the solution to the complimentary equation to find the
general solution
c) Use the initial conditions to find the specific solution

.1.) Modelling using second order differential equations
a) Find the ODE that models of the motion of the dumped spring
mass system with mass m=1, damping coefficient c=3, and spring
constant k=25/4 under the influence of an external force F(t) = cos
(2t).
b) Find the solution of the initial value problem with x(0)=6,
x'(0)=0.
c) Sketch the graph of the long term displacement of the mass
m.

How can I convert a second orde ODE into a first-order coupled
equation in terms of the variables of X and P for a simple harmonic
oscillator using the Hamiltonian Equation?

I'm studying Erwin Kreyszig's advanced engineering Mathematics
and I have an homework, how can I solve this?
Solve the following initial value problem of 2nd ODE.
y''+0.2y'+0.26y = 1.22*e^(0.5x), y(0) = 3.5, y'(0) = 0.35

10.16: Write a user-defined MATLAB function that solves a
first-order ODE by applying the midpoint method (use the form of
second-order Runge-Kutta method, Eqs(10.65),(10.66)). For function
name and arguments use [x,y]=odeMIDPOINT(ODE,a,b,h,yINI). The input
argument ODE is a name for the function that calculates dy/dx. It
is a dummy name for the function that is imported into odeMIDPOINT.
The arguments a and b define the domain of the solution, h is step
size; yINI is initial value. The output arguments, x...

Solve the linear programming problem by the method of
corners.
Maximize P = 2x + 6y
subject to 2x + y ≤ 16
2x + 3y ≤ 24
y ≤ 6
x ≥ 0, y ≥ 0
The maximum is P = at (x, y) = .

Choose the correct answers
If y1 and y2 are two
solutions of a nonhomogeneous equation ayjj+
byj+ cy =f (x), then
their difference is a solution of the equation
ayjj+ byj+ cy =
0.
If f (x) is continuous everywhere, then there
exists a unique solution to the following initial value
problem.
f (x)yj=
y, y(0) = 0
The differential equation yjj +
t2yj −
y = 3 is linear.
There is a solution to the ODE
yjj+3yj+y...

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