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

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

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(dy)/(dx)=(3x)/(y+x^2y)

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

y = 3 ln (1 + x^{2}) + c_{1}, y = - 3 ln (1 + x^{2}) + c_{1}

Solution steps

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

Solve separable ODE:

y = 3 ln (1 + x^{2}) + c_{1}, y = - 3 ln (1 + x^{2}) + c_{1}

y = 3 ln (1 + x^{2}) + c_{1}, y = - 3 ln (1 + x^{2}) + c_{1}

\frac{\partial}{\partial x} (\frac{x - y}{x ^{2} + y ^{2}})

\int \frac{1 - x}{x ^{2} + 3 x + 2} d x

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

\int (5 x^{4} + 3 x^{3} - 2) d x

\int (cos (θ) - 2 sin (θ))^{2} d θ

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