Solving Inhomogeneous Differential Equations with ODE Particular Solution

[sleventh]

Hi all,
I've been staring at this for much to long:

y''+2y=6x+4

what were going over now is homogeneous and inhomogeneous differential equations but i can't seem to think of a method for solving this one other then by inspection. Thank you very much for your help.

 

[D H]

In this case, inspection works quite nicely. What's wrong with that?

If you don't like that, you can try the method of undetermined coefficients or try to find an annihilator of the right hand side.

 

[sleventh]

i don't like inspection since i haven't found a function that would fit! haha. but thank you, at least i'll stop my wild goose chance for adaptations on integrating factor or separation

 

[sleventh]

AH! 2+3x works, silly me.