What is the solution for y^'-xy=xy^{3/2} ?

The solution for y^'-xy=xy^{3/2} is y= 1/(e^{(-x^2-4c_{1))/2}-2e^{(-x^2-4c_{1})/4}+1}

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y^'-xy=xy^{3/2}

y^{^{'}} - x y = x y^{\frac{3}{2}}

y = \frac{1}{e ^{\frac{- x ^{2} - 4 c _{1}}{2}} - 2 e ^{\frac{- x ^{2} - 4 c _{1}}{4}} + 1}

Solution steps

y^{'} (x) - x y = x y^{\frac{3}{2}}

Solve Bernoulli ODE:

y = \frac{1}{e ^{\frac{- x ^{2} - 4 c _{1}}{2}} - 2 e ^{\frac{- x ^{2} - 4 c _{1}}{4}} + 1}

y = \frac{1}{e ^{\frac{- x ^{2} - 4 c _{1}}{2}} - 2 e ^{\frac{- x ^{2} - 4 c _{1}}{4}} + 1}

\frac{1}{x}

y = 9 arctan (x - 1 + x^{2})

\int \frac{x}{x - 5} d x

\int arctan (y) d y

f (x) = \frac{1}{2 x}

What is the solution for y^'-xy=xy^{3/2} ?
The solution for y^'-xy=xy^{3/2} is y= 1/(e^{(-x^2-4c_{1))/2}-2e^{(-x^2-4c_{1})/4}+1}