How do I solve $y''+y'+7y=t$? How do I solve $y''+y'+7y=t$ where $y(0)=0$ and $y'(0)=0$ $(t\geq 0)$?
I tried to solve this by Laplace transformation, but I couldn't find the inverse of $1/(s^2(s^2+s+7))$.
How would I solve this?

Hint: The charactaristic equation is $$1+x+7x^2=0$$
Solve it. You will find two complex roots. 

Then find a particular solution. 
A hint for finding it: 


*

*What happens when you put $y=\frac{1}{7}t$? 

*How can you prevent that?



Method 1. Substiute $at+b$ to get $7at+7b+a=t$. Thus $7a=1$, thus $a=\frac{1}{7}$. Then $7b+a=0$,  thus $b=-\frac{1}{49}$.
Therefore the particular solution is $\frac{1}{7}t-\frac{1}{49}$
