What is the solution for y^{''}-1/t y^'+2/(t^2)y=0 ?

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

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y^{''}-1/t y^'+2/(t^2)y=0

y^{^{''}} - \frac{1}{t} y^{^{'}} + \frac{2}{t ^{2}} y = 0

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

Solution steps

y^{''} (t) - \frac{1}{t} y^{'} (t) + \frac{2}{t ^{2}} y = 0

Solve linear ODE:

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

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

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