What is the solution for (dy)/(dx)=x^2-y-2,y(0)=1 ?

The solution for (dy)/(dx)=x^2-y-2,y(0)=1 is y=x^2-2x+1/(e^x)

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(dy)/(dx)=x^2-y-2,y(0)=1

\frac{d y}{d x} = x^{2} - y - 2, y (0) = 1

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

Solution steps

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

Solve linear ODE:

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

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

\int 5 x^{\frac{3}{2}} + 2 x d x

\int (1 - 2 x^{2} - \frac{4}{x ^{- 3}}) x^{- 3} d x

\int (7 x^{2} - 12 x) e^{2 x} d x

x \to - 2 - lim (- 3 x^{2} + 2)

What is the solution for (dy)/(dx)=x^2-y-2,y(0)=1 ?
The solution for (dy)/(dx)=x^2-y-2,y(0)=1 is y=x^2-2x+1/(e^x)