What is the solution for (dy)/(dx)=yx^3-xy ?

The solution for (dy)/(dx)=yx^3-xy is y=e^{(x^4)/4-(x^2)/2+c_{1}}

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(dy)/(dx)=yx^3-xy

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

y = e^{\frac{x ^{4}}{4} - \frac{x ^{2}}{2} + c_{1}}

Solution steps

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

Solve separable ODE:

y = e^{\frac{x ^{4}}{4} - \frac{x ^{2}}{2} + c_{1}}

y = e^{\frac{x ^{4}}{4} - \frac{x ^{2}}{2} + c_{1}}

2 x y + 6 x + (x^{2} - 4) \frac{d y}{d x} = 0

\frac{d y}{d x} = \frac{6 - x ^{2}}{2 y ^{3}}

\frac{d y}{d x} = \frac{x}{y}, y (0) = - 6

\frac{d y}{d x} = 10 x sec (y)

What is the solution for (dy)/(dx)=yx^3-xy ?
The solution for (dy)/(dx)=yx^3-xy is y=e^{(x^4)/4-(x^2)/2+c_{1}}