What is the solution for x^5(dy)/(dx)=3x^2sqrt(1-y^2) ?

The solution for x^5(dy)/(dx)=3x^2sqrt(1-y^2) is y=sin(-3/(2x^2)+c_{1})

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x^5(dy)/(dx)=3x^2sqrt(1-y^2)

x^{5} \frac{d y}{d x} = 3 x^{2} 1 - y^{2}

y = sin (- \frac{3}{2 x ^{2}} + c_{1})

Solution steps

x^{5} \frac{d y}{d x} = 3 x^{2} 1 - y^{2}

Solve separable ODE:

y = sin (- \frac{3}{2 x ^{2}} + c_{1})

y = sin (- \frac{3}{2 x ^{2}} + c_{1})

x^{3} + 8 y \frac{d y}{d x} = 0

\frac{d y}{d x} = y (8 x^{2} + 1)

\frac{1}{y ^{2}} - \frac{3 x}{y ^{3}} \frac{d y}{d x} = 0

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

y^{2} y^{^{'}} = 2 (t + t y^{3}) e^{t^{2}}, y (0) = 0

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