Answer to Question #271007 in Differential Equations for Aysu

Differential Equations

Question #271007

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

Expert's answer

"(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"

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