How can a first-order linear differential equation be solved?

Answer 1

If you have a first order linear equation, there are many approachs i.e.

separable variable

constant coefficients

undetermined coefficients

...

You actually need to classify it in more depth e.g.

t^2y''+ty'+y=x^2 is a second-order-linear-nonhomogeneous-cauchy-euler-ordinary differential equation

We would then have again a few options, which we perform trial by error to find the best fit