What is the solution for (x+2y)dx+(2x-3y)dy=0 ?

The solution for (x+2y)dx+(2x-3y)dy=0 is y=-(-2x+sqrt(7x^2-c_{1)})/3 ,y=(2x+sqrt(7x^2-c_{1)})/3

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(x+2y)dx+(2x-3y)dy=0

(x + 2 y) d x + (2 x - 3 y) d y = 0

y = - \frac{- 2 x + 7 x ^{2} - c _{1}}{3}, y = \frac{2 x + 7 x ^{2} - c _{1}}{3}

Solution steps

(x + 2 y) d x + (2 x - 3 y) d y = 0

Solve exact ODE:

y = - \frac{- 2 x + 7 x ^{2} - c _{1}}{3}, y = \frac{2 x + 7 x ^{2} - c _{1}}{3}

y = - \frac{- 2 x + 7 x ^{2} - c _{1}}{3}, y = \frac{2 x + 7 x ^{2} - c _{1}}{3}

What is the solution for (x+2y)dx+(2x-3y)dy=0 ?
The solution for (x+2y)dx+(2x-3y)dy=0 is y=-(-2x+sqrt(7x^2-c_{1)})/3 ,y=(2x+sqrt(7x^2-c_{1)})/3