Second order differential equation - Drawing circuit

[jusb3]

Homework Statement

"Solve differential equation y''+y=2*cos x. Draw circuit of the equation and think about the strange behavior of the current."

The attempt at a solution

I was able to solve the equation, but I have no idea how to draw circuit about it, we haven't gone
through this at lessons.

Solution:

y(x)=C_1*e^(ix)+C_2*e^(-ix)+x*sin x

 

[Mark44]

Homework Statement

"Solve differential equation y''+y=2*cos x. Draw circuit of the equation and think about the strange behavior of the current."

The attempt at a solution

I was able to solve the equation, but I have no idea how to draw circuit about it, we haven't gone
through this at lessons.

Solution:

y(x)=C_1*e^(ix)+C_2*e^(-ix)+x*sin x

For the drawing part, think about what the coefficients of the DE mean in regard to the capacitor, coil, and resister of an LRC circuit. Since there's no y' term, one of these components is missing in your circuit.

For your solution, you have e^ix and e^-ix as the basic functions that are the solutions to the homogeneous problem. You could also have used cos(x) and sin(x). Since e^ix = cos(x) + i*sin(x), and e^-ix = cos(x) - i*sin(x), it's not too hard to find that cos(x) = (e^ix + e^-ix)/2 and something similar for sin(x).