lukaszskowron96
New member
- Joined
- Oct 16, 2018
- Messages
- 1
Hi, the non-homogeneous ODE I have to solve is this:
d^2(y)/dt^2 + y = -cos(t) with y(0) = 1 and y'(0) = 0
Here's the procedure I applied.
1) Find the complimentary function of homogeneous ODE:
d^2(y)/dt^2 + y = 0
It's a simple harmonic oscillator, so the solution is:
y_CF = A*cos(t) + B*sin(t) = 0 using the BCs
2) Find the particular integral:
d^2(y)/dt^2 + y = -cos(t)
and here I don't understand why the y_PI = A*x*sin(t) + B*x*cos(t) ??
The rest of the solution process is trivial.
d^2(y)/dt^2 + y = -cos(t) with y(0) = 1 and y'(0) = 0
Here's the procedure I applied.
1) Find the complimentary function of homogeneous ODE:
d^2(y)/dt^2 + y = 0
It's a simple harmonic oscillator, so the solution is:
y_CF = A*cos(t) + B*sin(t) = 0 using the BCs
2) Find the particular integral:
d^2(y)/dt^2 + y = -cos(t)
and here I don't understand why the y_PI = A*x*sin(t) + B*x*cos(t) ??
The rest of the solution process is trivial.