This is a qn on differential eqn?

Question

differential eqn:x(dy/dx) - y = x² + 1

show that general solution is y = x² + Cx - 1 (C is an arbitrary constant)

thx (:

Answer 1

dy/dx - (y/x) = x + 1/x

use an integrating factor: e^∫(-1/x) dx = e^-lnx = 1/x

(1/x) dy/dx - (y/x^2) = 1 + 1/x^2

D[(1/x) * y] = 1 + 1/x^2

(1/x) y =  x - 1/x + C

.. . .

y = x^2 - 1 + Cx

.. . .. .