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

The solution for (2x+3y)dx+(3x+2y)dy=0 is y=(-3x+sqrt(5x^2+c_{1)})/2 ,y=(-3x-sqrt(5x^2+c_{1)})/2

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

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

y = \frac{- 3 x + 5 x ^{2} + c _{1}}{2}, y = \frac{- 3 x - 5 x ^{2} + c _{1}}{2}

Solution steps

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

Solve exact ODE:

y = \frac{- 3 x + 5 x ^{2} + c _{1}}{2}, y = \frac{- 3 x - 5 x ^{2} + c _{1}}{2}

y = \frac{- 3 x + 5 x ^{2} + c _{1}}{2}, y = \frac{- 3 x - 5 x ^{2} + c _{1}}{2}

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What is the solution for (2x+3y)dx+(3x+2y)dy=0 ?
The solution for (2x+3y)dx+(3x+2y)dy=0 is y=(-3x+sqrt(5x^2+c_{1)})/2 ,y=(-3x-sqrt(5x^2+c_{1)})/2