What is the solution for -5t^2y^{''}+ty^'+8y=0 ?

The solution for -5t^2y^{''}+ty^'+8y=0 is y=(c_{1})/(t^{4/5)}+c_{2}t^2

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-5t^2y^{''}+ty^'+8y=0

- 5 t^{2} y^{^{''}} + t y^{^{'}} + 8 y = 0

y = \frac{c _{1}}{t ^{\frac{4}{5}}} + c_{2} t^{2}

Solution steps

- 5 t^{2} y^{''} (t) + t y^{'} (t) + 8 y = 0

Solve linear ODE:

y = \frac{c _{1}}{t ^{\frac{4}{5}}} + c_{2} t^{2}

y = \frac{c _{1}}{t ^{\frac{4}{5}}} + c_{2} t^{2}

\frac{3}{x}, 12 x, \frac{1}{3} x

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What is the solution for -5t^2y^{''}+ty^'+8y=0 ?
The solution for -5t^2y^{''}+ty^'+8y=0 is y=(c_{1})/(t^{4/5)}+c_{2}t^2