What is the solution for (dy)/(dx)=x^2(1+y),y(0)=3 ?

The solution for (dy)/(dx)=x^2(1+y),y(0)=3 is y=4e^{(x^3)/3}-1

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(dy)/(dx)=x^2(1+y),y(0)=3

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

y = 4 e^{\frac{x ^{3}}{3}} - 1

Solution steps

\frac{d y}{d x} = x^{2} (1 + y)

Solve separable ODE:

y = 4 e^{\frac{x ^{3}}{3}} - 1

y = 4 e^{\frac{x ^{3}}{3}} - 1

x \to 0 lim (csc (x) ln (x + 1))

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y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} - 91 x e^{x}

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What is the solution for (dy)/(dx)=x^2(1+y),y(0)=3 ?
The solution for (dy)/(dx)=x^2(1+y),y(0)=3 is y=4e^{(x^3)/3}-1