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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} = x (1 + y)^{2}

\frac{d y}{d x} = \frac{x ln ( x )}{y ^{2}}

\frac{d y}{d x} = \frac{sin ( x )}{sin ( y )}

H (x) (x)^{2} x^{2} d x - 2 x^{3} d H (x) = 0

y^{^{'}} = x (10 - y)

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