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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int \frac{x ^{2}}{( x - 1 ) ^{3}} d x

\frac{\partial}{\partial x} (\frac{5}{e ^{x}})

y^{^{'}} + 4 y = 3 sin (2 t)

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

(- 1, 4), (- 3, - 2)

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