# Thread: 4th order ode: private solution

1. ## 4th order ode: private solution

Dear all
Hi,

I seek the solution of the 4th order ordinary differential equation as follows:

d^4(y) / dx^4 + G * y = H

for the homogenous relation which is:
d^4(y) / dx^4 + G * y = 0
or
G=4*b^4
d^4(y) / dx^4 + 4*b^4 * y = 0

we assume the solution of the bellow form:
y=exp(b*x)*(A*cos(b*x)+B*sin(b*x))+exp(-b*x)*(C*cos(b*x)+D*sin(b*x))

Now what is the private solution for the inhomogenous equation?

2. ## Re: 4th order ode: private solution

Originally Posted by nsvcivil
Dear all
Hi,

I seek the solution of the 4th order ordinary differential equation as follows:

d^4(y) / dx^4 + G * y = H

for the homogenous relation which is:
d^4(y) / dx^4 + G * y = 0
or
G=4*b^4
d^4(y) / dx^4 + 4*b^4 * y = 0

we assume the solution of the bellow form:
y=exp(b*x)*(A*cos(b*x)+B*sin(b*x))+exp(-b*x)*(C*cos(b*x)+D*sin(b*x))

Now what is the private solution for the inhomogenous equation?
Assuming $H$ is a constant, a particular integral is the constant function $y(x)=H/(4b^4)$

CB