Verify that the following functions y(x) are solutions of the given second order ODE and satisfy the given initial conditions.
y"+2y'+y=0; y(0)=1; y'(0)=1; y(x)=(1+2x)e^(-x). Some guidance would be very helpful.

Question

Verify that the following functions y(x) are solutions of the given second order ODE and satisfy the given initial conditions. 
y"+2y'+y=0; y(0)=1; y'(0)=1; y(x)=(1+2x)e^(-x). Some guidance would be very helpful.

anonymous · Answer

write the auxilliary equation and find D or m whatever you call it.

anonymous · Answer

you know how to write the equation.

anonymous · Answer

I think I figured it out. I just had to check the initial conditions with y(x) and y'(x) and make sure that they come out as y(0)=1 and y'(0)=1

anonymous · Answer

ok. if you need my help show me your work and i will guide you.

anonymous · Answer

I think I got this one. Thanks anyways.

anonymous · Answer

yw