What is the solution for y^{7/2}(dy)/(dx)-y^3=-y^{9/2} ?

The solution for y^{7/2}(dy)/(dx)-y^3=-y^{9/2} is y=\sqrt[3]{e^{-3x-3c_{1}}+2e^{(-3x-3c_{1})/2}+1}

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y^{7/2}(dy)/(dx)-y^3=-y^{9/2}

y^{\frac{7}{2}} \frac{d y}{d x} - y^{3} = - y^{\frac{9}{2}}

Solution steps

y^{\frac{7}{2}} \frac{d y}{d x} - y^{3} = - y^{\frac{9}{2}}

Solve separable ODE:

\frac{d y}{d x} x ln (x) - y = 0

y^{^{'}} = e^{7 x - 10 y}, y (0) = 0

y^{^{'}} csc (t) = \frac{- y ^{19}}{18}

\frac{d y}{d x} = \frac{- x}{y e ^{x^{2}}}

y \frac{d y}{d x} = \frac{( 9 x ^{3} - 1 )}{( 7 + y ^{2} )}

What is the solution for y^{7/2}(dy)/(dx)-y^3=-y^{9/2} ?
The solution for y^{7/2}(dy)/(dx)-y^3=-y^{9/2} is y=\sqrt[3]{e^{-3x-3c_{1}}+2e^{(-3x-3c_{1})/2}+1}