Find the general solution of the given differential equations, the largest interval over which the solution is defied and determine whether there are any transient terms in the solution.

I mainly need someone to check my answer and if they're wrong to help me correct the mistakes I made

I found the integrating factor to be

Multiplied both sides by integrating factor and integrated to get:

Largest interval I think would be (-∞, ∞) and I don't think there are any transient terms

Thanks in advance.