What is the solution for (dy)/(dx)=x^2(y-2),y(0)=4 ?

The solution for (dy)/(dx)=x^2(y-2),y(0)=4 is y=2e^{(x^3)/3}+2

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(dy)/(dx)=x^2(y-2),y(0)=4

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

y = 2 e^{\frac{x ^{3}}{3}} + 2

Solution steps

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

Solve separable ODE:

y = 2 e^{\frac{x ^{3}}{3}} + 2

y = 2 e^{\frac{x ^{3}}{3}} + 2

y^{^{'}} = e^{- y}, y (0) = 0

\frac{d y}{d x} = \frac{2}{3} x 1 - 9 y^{2}, y (0) = 0

\frac{d v}{d t} = \frac{2}{9} v

\frac{d}{d x} (x + y) = 1

(1 + e^{x}) y \cdot y^{^{'}} = e^{y}

What is the solution for (dy)/(dx)=x^2(y-2),y(0)=4 ?
The solution for (dy)/(dx)=x^2(y-2),y(0)=4 is y=2e^{(x^3)/3}+2