What is the solution for (4x-3y)dx+(2y-3x)dy=0 ?

The solution for (4x-3y)dx+(2y-3x)dy=0 is y=(3x+sqrt(x^2+c_{1)})/2 ,y=(3x-sqrt(x^2+c_{1)})/2

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(4x-3y)dx+(2y-3x)dy=0

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

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

Solution steps

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

Solve exact ODE:

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

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

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What is the solution for (4x-3y)dx+(2y-3x)dy=0 ?
The solution for (4x-3y)dx+(2y-3x)dy=0 is y=(3x+sqrt(x^2+c_{1)})/2 ,y=(3x-sqrt(x^2+c_{1)})/2