What is the solution for (dy)/(dx)=x^2-1/2 y ?

The solution for (dy)/(dx)=x^2-1/2 y is y=2x^2-16(1/2 x-1)+(c_{1})/(e^{x/2)}

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(dy)/(dx)=x^2-1/2 y

\frac{d y}{d x} = x^{2} - \frac{1}{2} y

y = 2 x^{2} - 16 (\frac{1}{2} x - 1) + \frac{c _{1}}{e ^{\frac{x}{2}}}

Solution steps

\frac{d y}{d x} = x^{2} - \frac{1}{2} y

Solve linear ODE:

y = 2 x^{2} - 16 (\frac{1}{2} x - 1) + \frac{c _{1}}{e ^{\frac{x}{2}}}

y = 2 x^{2} - 16 (\frac{1}{2} x - 1) + \frac{c _{1}}{e ^{\frac{x}{2}}}

\frac{\partial}{\partial x} (x^{3} + 2)

\frac{d}{d x} (x^{4} e^{- 3 x})

x^{2} 8 x - 7

(- 8, - 3), (- 24, 1)

\frac{\partial}{\partial x} (5 x^{4} y^{2} + x y^{3} + 4)

What is the solution for (dy)/(dx)=x^2-1/2 y ?
The solution for (dy)/(dx)=x^2-1/2 y is y=2x^2-16(1/2 x-1)+(c_{1})/(e^{x/2)}