What is the solution for y^{5/2}(dy)/(dx)-y^2=-y^{7/2} ?

The solution for y^{5/2}(dy)/(dx)-y^2=-y^{7/2} is y=\sqrt[3]{e^{-3x-3c_{1}}+2e^{(-3x-3c_{1})/2}+1}

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y^{5/2}(dy)/(dx)-y^2=-y^{7/2}

y^{\frac{5}{2}} \frac{d y}{d x} - y^{2} = - y^{\frac{7}{2}}

Solution steps

y^{\frac{5}{2}} \frac{d y}{d x} - y^{2} = - y^{\frac{7}{2}}

Solve separable ODE:

P^{^{'}} = k P (t)

x y^{^{'}} y + 4 = 0

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

\frac{d y}{d x} = 12 x y

y^{^{'}} - a \cdot y = 0

What is the solution for y^{5/2}(dy)/(dx)-y^2=-y^{7/2} ?
The solution for y^{5/2}(dy)/(dx)-y^2=-y^{7/2} is y=\sqrt[3]{e^{-3x-3c_{1}}+2e^{(-3x-3c_{1})/2}+1}