Thread: second order ODE

Hello,

I have this problem:

solve this ODE



so the Characteristic Equation is going to be:


i'm going to get a complex root correct? I'm really unsure on how to approach complex roots.

Originally Posted by dlbsd

Hello,

I have this problem:

solve this ODE



so the Characteristic Equation is going to be:


i'm going to get a complex root correct? I'm really unsure on how to approach complex roots.

If the roots of the auxillary equation are then the homogenous solution to the differential equation is .

Since, u''=-u

A function differentiated twice gives the negative of the same function, so it can be either A*cosine(bx) or B*sine(bx). By principle of superposition of the results (which is saying if two solutions are there bundle them up together)... u(x)=A cos (bx) + B sin (bx)