Question

2x dy/dx+y=6x^3
How to solve ?

Answer 1

2xy' + y = 6x^3
y' + (1/2x)y = 3x^2

Look for an integrating factor:
u(x) = e^(∫1/(2x) dx) = √x

Now multiply by that and we have

√x y' + y/(2√x) = 3x^(5/2)

(√x y)' = 3x^(5/2)
√x y = 6/7 x^(7/2) + c
y = 6/7 x^3 + c/√x

Answer 2

Thanx a lot steve :)