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

The solution for t^2y^{''}+ty^'+y=0 is y=c_{1}cos(ln(t))+c_{2}sin(ln(t))

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

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

y = c_{1} cos (ln (t)) + c_{2} sin (ln (t))

Solution steps

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

Solve linear ODE:

y = c_{1} cos (ln (t)) + c_{2} sin (ln (t))

y = c_{1} cos (ln (t)) + c_{2} sin (ln (t))

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What is the solution for t^2y^{''}+ty^'+y=0 ?
The solution for t^2y^{''}+ty^'+y=0 is y=c_{1}cos(ln(t))+c_{2}sin(ln(t))