What is the solution for y^'=x^2y-x^2y^2,y(0)=17 ?

The solution for y^'=x^2y-x^2y^2,y(0)=17 is y=(17e^{(x^3)/3})/(17e^{(x^3)/3)-16}

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y^'=x^2y-x^2y^2,y(0)=17

y^{^{'}} = x^{2} y - x^{2} y^{2}, y (0) = 17

y = \frac{17 e ^{\frac{x ^{3}}{3}}}{17 e ^{\frac{x ^{3}}{3}} - 16}

Solution steps

y^{'} (x) = x^{2} y - x^{2} y^{2}

Solve separable ODE:

y = \frac{17 e ^{\frac{x ^{3}}{3}}}{17 e ^{\frac{x ^{3}}{3}} - 16}

y = \frac{17 e ^{\frac{x ^{3}}{3}}}{17 e ^{\frac{x ^{3}}{3}} - 16}

f (x) = x + \frac{5}{x}

\frac{d}{d x} (\frac{2 x - 7}{3 x - 2})

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What is the solution for y^'=x^2y-x^2y^2,y(0)=17 ?
The solution for y^'=x^2y-x^2y^2,y(0)=17 is y=(17e^{(x^3)/3})/(17e^{(x^3)/3)-16}