General and particular solution

Question

Show complete solution and use equation function.

1. Find the general solution of xdx = 9x²dx- ydy.

2. Find the general solution to the equation (cos y + 2) dy/dx = 2x.

Answer 1

1. ydy = (9x² - x)dx; ∫ydy = ∫(9x² - x)dx; y²/2 = 3x³ - x²/2 + C/2; y² = 6x³ - x² + C
2. (cosy + 2)dy = 2x/dx; ∫(cosy + 2)dy = ∫2xdx; siny + 2y = x² + C