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

The solution for (dy)/(dx)=x^3-2y is y=(x^3)/2-(3(2x^2-2x+1))/8+(c_{1})/(e^{2x)}

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

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

y = \frac{x ^{3}}{2} - \frac{3 ( 2 x ^{2} - 2 x + 1 )}{8} + \frac{c _{1}}{e ^{2 x}}

Solution steps

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

Solve linear ODE:

y = \frac{x ^{3}}{2} - \frac{3 ( 2 x ^{2} - 2 x + 1 )}{8} + \frac{c _{1}}{e ^{2 x}}

y = \frac{x ^{3}}{2} - \frac{3 ( 2 x ^{2} - 2 x + 1 )}{8} + \frac{c _{1}}{e ^{2 x}}

What is the solution for (dy)/(dx)=x^3-2y ?
The solution for (dy)/(dx)=x^3-2y is y=(x^3)/2-(3(2x^2-2x+1))/8+(c_{1})/(e^{2x)}