What is the solution for 10x^2y+2x^3y^'-16y=0,y(1)=1 ?

The solution for 10x^2y+2x^3y^'-16y=0,y(1)=1 is y=(e^{\frac{-4+4x^2)/(x^2)}}{x^5}

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10x^2y+2x^3y^'-16y=0,y(1)=1

10 x^{2} y + 2 x^{3} y^{^{'}} - 16 y = 0, y (1) = 1

y = \frac{e ^{\frac{- 4 + 4 x ^{2}}{x ^{2}}}}{x ^{5}}

Solution steps

10 x^{2} y + 2 x^{3} y^{'} (x) - 16 y = 0

Solve separable ODE:

y = \frac{e ^{\frac{- 4 + 4 x ^{2}}{x ^{2}}}}{x ^{5}}

y = \frac{e ^{\frac{- 4 + 4 x ^{2}}{x ^{2}}}}{x ^{5}}

y \cdot y^{^{'}} = 3

\frac{d y}{d x} + \frac{1 + y ^{3}}{x y ^{2} ( 1 + x ^{2} )} = 0

\frac{d y}{d x} = - \frac{2}{8} x^{6} y^{2}

\frac{d x}{d t} = \frac{2}{x e ^{t + 4 x}}

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

What is the solution for 10x^2y+2x^3y^'-16y=0,y(1)=1 ?
The solution for 10x^2y+2x^3y^'-16y=0,y(1)=1 is y=(e^{\frac{-4+4x^2)/(x^2)}}{x^5}