Second order differential equation

[eidbadr]

hello i need some help here!

solve:

x''+3x'+2x=1/(1+e^t)

well ok the homogeneous solution is c1*e^t+c2*e^2t
but how to determine the particular solution Xp!

 

[rock.freak667]

Try using the variation of parameters method

 

[HallsofIvy]

If the right hand side were a function of the kind one gets as a solution to a "homogenoous linear equation with constant coefficients"- polynomial, exponentian, sine and cosine, or combinations of those- then you could try "undetermined coefficients' but since it is not you will need to try "variation of parameters" as rock.freak667 suggested.

 

[eidbadr]

thanks that worked,

if you could give me a hint for this one

t*x'=x+sqrt(x^2-t^2)