Anyone here good with non-homogeneous second order differential equations??

Question

anonymous · Answer

wolframalpha.com is really good for checking answers on differential equations. I'm not great at them but I would suggest that website.

nikvist · Answer

I don't see anyone

anonymous · Answer

my issue is finding the particular solution for the ones with complex roots of the characteristic equation of the homogeneous part

nikvist · Answer

ok! write that diff. equation

anonymous · Answer

y''+2y'+2y=10cos(2x)

anonymous · Answer

so the homogenous part is y=e^(-x)(Ccos(x)+Dsin(x))

nikvist · Answer

$$y_P=A\cos{2x}+B\sin{2x}$$
find $$y'_P\quad,\quad y''_P$$ put in diff. equation, and you will get A and B.

anonymous · Answer

yehhh just tried this its working out very nicely thank you

phi · Answer

You can set yp= A cos(2x) + B cos(2x) , plug into the diff. eq. and match terms
to find A, B
yp is the linear combination of all deviates of cos(2x) (ignoring coeffs)

phi · Answer

*derivatives