What is the solution for y^'=sqrt(x)y^{3/2} ?

The solution for y^'=sqrt(x)y^{3/2} is y=(36)/(4x^3+12c_{1)x^{3/2}+9c_{1}^2}

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y^'=sqrt(x)y^{3/2}

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

y = \frac{36}{4 x ^{3} + 12 c _{1} x ^{\frac{3}{2}} + 9 c _{1}^{2}}

Solution steps

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

Solve separable ODE:

y = \frac{36}{4 x ^{3} + 12 c _{1} x ^{\frac{3}{2}} + 9 c _{1}^{2}}

y = \frac{36}{4 x ^{3} + 12 c _{1} x ^{\frac{3}{2}} + 9 c _{1}^{2}}

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

x \frac{d y}{d x} = e^{9 y + x}, x > 0

(1 + y^{2}) cos (x) d x - \frac{1}{x} d y = 0, y (0) = \frac{π}{4}

y^{^{'}} = x^{3} y^{3}

\frac{d x}{d t} = a x

What is the solution for y^'=sqrt(x)y^{3/2} ?
The solution for y^'=sqrt(x)y^{3/2} is y=(36)/(4x^3+12c_{1)x^{3/2}+9c_{1}^2}