# Quick Differential equation question

• September 14th 2012, 08:24 AM
Dragonkiller
Quick Differential equation question
Heys I was wondering if anyone could guide me through this question:
Let a be a real number. Find the general solution of the differential equation.
y''' + y'' = a
Thanks :)
• September 14th 2012, 08:35 AM
topsquark
Re: Quick Differential equation question
Quote:

Originally Posted by Dragonkiller
Heys I was wondering if anyone could guide me through this question:
Let a be a real number. Find the general solution of the differential equation.
y''' + y'' = a
Thanks :)

The characteristic equation will be
m^3 + m^2 = 0

m^2(m + 1) = 0

Two zeros at 0, and one at -1.

Can you finish from here?

-Dan
• September 15th 2012, 04:49 AM
Dragonkiller
Re: Quick Differential equation question
Where do I go after finding the homogeneous solution?
• September 15th 2012, 05:34 AM
MarkFL
Re: Quick Differential equation question
You could then assume a particular solution of the form:

$y_p(x)=x^s(A)$

Where the natural number s is chosen to be the smallest value so that no term in the particular solution is a solution to the corresponding homogeneous equation. Hence, let:

$y_p(x)=Ax^2$

and use the method of undetermined coefficients to determine A.