Hello, Mathsnewbie!

You should have been taught to recognize and solve different forms.

Separate variables: .

Integrate: . . . . etc.

This requires an Integrating Factor . . .

Divide by

. . Then: .

Multiply by

And we have: .

Integrate: . . . . etc.

The characteristic equation is: .

. . which factors: .

. . and has roots: .

Therefore: .