Find the particular solution to Dy/Dx = 3x^2 + 1

[Creaturemagic]

Find the particular solution to Dy/Dx = 3x^2 + 1 when y(0) = 3

I've looked everywhere for steps to solve this problem, and every website I have been to has taught me how to do a question like this when each side has a Y (is separable) but I can't find out how to do one like the question above.

I don't need it to be done for me, I just would love to know the steps I should take in solving it.

Thanks!

 

[Simon Bridge]

Starting from: $$\frac{dy}{dx} = f(x)$$ ... multiply both sides by ##dx##: $$dy = f(x)dx$$ ... integrate both sides: $$\int dy = \int f(x)dx$$

Although - Dy/Dx may not mean dy/dx in this case.