What is the solution for t^2y^{''}+6ty^'+6y=0 ?

The solution for t^2y^{''}+6ty^'+6y=0 is y=(c_{1})/(t^2)+(c_{2})/(t^3)

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t^2y^{''}+6ty^'+6y=0

t^{2} y^{^{''}} + 6 t y^{^{'}} + 6 y = 0

y = \frac{c _{1}}{t ^{2}} + \frac{c _{2}}{t ^{3}}

Solution steps

t^{2} y^{''} (t) + 6 t y^{'} (t) + 6 y = 0

Solve linear ODE:

y = \frac{c _{1}}{t ^{2}} + \frac{c _{2}}{t ^{3}}

y = \frac{c _{1}}{t ^{2}} + \frac{c _{2}}{t ^{3}}

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What is the solution for t^2y^{''}+6ty^'+6y=0 ?
The solution for t^2y^{''}+6ty^'+6y=0 is y=(c_{1})/(t^2)+(c_{2})/(t^3)