What is the solution for 3x^2y^2(dy)/(dx)=2x-1 ?

The solution for 3x^2y^2(dy)/(dx)=2x-1 is y=\sqrt[3]{(2xln(x)+1+3c_{1}x)/x}

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3x^2y^2(dy)/(dx)=2x-1

3 x^{2} y^{2} \frac{d y}{d x} = 2 x - 1

Solution steps

3 x^{2} y^{2} \frac{d y}{d x} = 2 x - 1

Solve separable ODE:

\frac{d y}{d x} = \frac{2 x sin ^{2} ( y )}{( x ^{2} + 10 ) cos ( y )}

y^{2} d x + d y = 0

v^{2} y^{2} d y + v y^{3} d v + 2 v^{2} y^{2} d y + y^{2} d y = 0

\frac{d y}{d x} = 3 y - 1

\frac{d x}{d y} = e^{2 x + 3 y}

What is the solution for 3x^2y^2(dy)/(dx)=2x-1 ?
The solution for 3x^2y^2(dy)/(dx)=2x-1 is y=\sqrt[3]{(2xln(x)+1+3c_{1}x)/x}