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

The solution for (dy)/(dx)=2yx+yx^2 is y=e^{(x^3)/3+x^2+c_{1}}

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(dy)/(dx)=2yx+yx^2

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

y = e^{\frac{x ^{3}}{3} + x^{2} + c_{1}}

Solution steps

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

Solve separable ODE:

y = e^{\frac{x ^{3}}{3} + x^{2} + c_{1}}

y = e^{\frac{x ^{3}}{3} + x^{2} + c_{1}}

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\frac{d}{d x} (x (4 - x^{2}))

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

x \to 0 lim (\frac{3}{x ( 2 \cdot x + 1 )})

\frac{\partial}{\partial x} (x^{3} + y^{3} - 6 x y)

What is the solution for (dy)/(dx)=2yx+yx^2 ?
The solution for (dy)/(dx)=2yx+yx^2 is y=e^{(x^3)/3+x^2+c_{1}}