Inhomogeneous equation

**AkilMAI** · April 30th 2011, 10:13 AM

How can I solve this equation $x''-x=(1+e^{t})^{-1}$ using the method of variation of parameters?Using the auxiliary equation the roots are $r_{1}=0$ and $r_{2}=1$ .
I don't know if I'm suppose to look for a solution of the form $x(t)=p+q*e^{x}$ manly because the initial equation has o 1+... after the equal sign .Can someone please help me?

**topsquark** · April 30th 2011, 04:57 PM

Originally Posted by AkilMAI

How can I solve this equation $x''-x=(1+e^{t})^{-1}$ using the method of variation of parameters?Using the auxiliary equation the roots are $r_{1}=0$ and $r_{2}=1$ .
I don't know if I'm suppose to look for a solution of the form $x(t)=p+q*e^{x}$ manly because the initial equation has o 1+... after the equal sign .Can someone please help me?

I'm not clear on how well you know the method, so I'll just say this for now. Recheck your solution to the homogeneous equation. m^2 - 1 = 0 gives what as solutions?

-Dan

**AkilMAI** · April 30th 2011, 05:31 PM

m1=1 and m2=-1....I don't know why I had the impression that the equation is x''-x'=... and not x''-x=...
I know that this method is called variation of parameters manly because we have varied the usual parameters
,A and B for instance, and made them functions x(t)=u1(t)x1(t)+u2(t)x2(t)

**AkilMAI** · May 1st 2011, 12:20 PM

but still I'm having trouble picking a solution to solve this

**topsquark** · May 1st 2011, 01:45 PM

Originally Posted by AkilMAI

m1=1 and m2=-1....I don't know why I had the impression that the equation is x''-x'=... and not x''-x=...
I know that this method is called variation of parameters manly because we have varied the usual parameters
,A and B for instance, and made them functions x(t)=u1(t)x1(t)+u2(t)x2(t)

Originally Posted by AkilMAI

but still I'm having trouble picking a solution to solve this

Since m = 1 and m = - 1 you know that the homogeneous solutions are
$x_1(t) = e^t~\text{ and }~x_2(t) = e^{-t}$

So your proposed particular solution will be
$x_p(t) = u_1(t)e^t + u_2(t)e^{-t}$

Can you work from there?

-Dan

Thread: Inhomogeneous equation

LinkBack

Thread Tools

Display

Inhomogeneous equation

Similar Math Help Forum Discussions

Second order non linear inhomogeneous differential equation.. :(

Inhomogeneous electromagnetic wave equation

Solving a second-order inhomogeneous differential equation

inhomogeneous linear differential equation

Second Order Inhomogeneous Differential Equation

Search Tags