Answer to Question #271007 in Differential Equations for Aysu

Question

Solve the equation in exact differentials: (3x²+2y)dx+(2x-3)dy=0

Answer 1

$(3x^2+2y)_y=(2x-3)_x=2$

$F=\int (3x^2+2y)dx=x^3+2xy+g(y)$

$F_y=2x+g'(y)=2x-3$

$g'(y)=-3$

$g(y)=-3y+c$

$F=x^3+2xy-3y+c$

$x^3+2xy-3y+c=0$