What is the solution for t^2y^{''}+19ty^'+81y=0 ?

The solution for t^2y^{''}+19ty^'+81y=0 is y=(c_{1})/(t^9)+(c_{2}ln(t))/(t^9)

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t^2y^{''}+19ty^'+81y=0

t^{2} y^{^{''}} + 19 t y^{^{'}} + 81 y = 0

y = \frac{c _{1}}{t ^{9}} + \frac{c _{2} ln ( t )}{t ^{9}}

Solution steps

t^{2} y^{''} (t) + 19 t y^{'} (t) + 81 y = 0

Solve linear ODE:

y = \frac{c _{1}}{t ^{9}} + \frac{c _{2} ln ( t )}{t ^{9}}

y = \frac{c _{1}}{t ^{9}} + \frac{c _{2} ln ( t )}{t ^{9}}

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What is the solution for t^2y^{''}+19ty^'+81y=0 ?
The solution for t^2y^{''}+19ty^'+81y=0 is y=(c_{1})/(t^9)+(c_{2}ln(t))/(t^9)