Second-order linear homogeneous diff. eq. with constant coefficients
I have the following diff.eq. (d^2)y/d(x^2) + 2 dy/dx + y = 0 , but I don't have the answer, so could you please check.
The general solution that I got is y= e^(-x)[Ax+B]
If we have that x=0 when y=3 and dy/dx=1 , Then the particular solution is y= e^(-x)[4x+3]?
And another one, which is inhomogenous:
(d^2)y/d(x^2) + 2 dy/dx + y = x+2
General solution: y= e^(-x)[Ax+B] + x^2-4x+8
when x=0, y=3 and dy/dx=1
Particular solution: y= e^(-x)[10x-5] + x^2-4x+8
Sry but I don't have the nerves to type-write the full solutions,however I took pictures: ImageShack Album - 8 images
Does someone know a good online calculator for second order diff. eq ? I tried wolfram alpha but it seems that it doesn't solve these type of eqs.