# Second-order linear homogeneous diff. eq. with constant coefficients

• May 21st 2011, 07:00 AM
Tron
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.
• May 21st 2011, 07:37 AM
TheEmptySet
Quote:

Originally Posted by Tron
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.

Here is what wolfram alpha gives

dsolve y&#39;&#39;&#40;x&#41;&#43;2y&#39;&#40;x&#41;&#43; y&#40;x&#41;&#61;x&#43;2 - Wolfram|Alpha

You will need to solve for the arbitrary constants!
• May 21st 2011, 07:44 AM
topsquark
Quote:

Originally Posted by Tron
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.

Surely you can put your solutions through the differential equation to check them?

Your answer to the homogeneous equation is correct, but the particular solution for the inhomogeneous equation is wrong. Try plugging your particular solution back into the inhomogeneous equation again. Or note that the particular solution will be of the form ax + b, not a quadratic.

-Dan
• May 21st 2011, 10:43 AM
Tron
Quote:

Originally Posted by topsquark
Surely you can put your solutions through the differential equation to check them?

Your answer to the homogeneous equation is correct, but the particular solution for the inhomogeneous equation is wrong. Try plugging your particular solution back into the inhomogeneous equation again. Or note that the particular solution will be of the form ax + b, not a quadratic.

-Dan

Hi

I checked with wolfram that my general solution to the inhomogenous is correct.
Whatever the values of A and B are for the particular solution, they won't change the second part of the equation ( the P.I.) , so it must stay x^2-4x+8 ?
• May 21st 2011, 02:01 PM
topsquark
Quote:

Originally Posted by Tron
Hi

I checked with wolfram that my general solution to the inhomogenous is correct.
Whatever the values of A and B are for the particular solution, they won't change the second part of the equation ( the P.I.) , so it must stay x^2-4x+8 ?