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

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

(2 x - 3 y) d x + (2 y - 3 x) 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 + (2 y - 3 x) 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}

\frac{d}{d x} (x^{2})

\frac{d}{d x} (arctan (4 x^{2} + 1))

\frac{1}{4 - x}

4 x - 1

y^{^{'}} = \frac{( x - 8 )}{x}

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