What is the solution for t^2y^{''}+7ty^'+9y=0 ?

The solution for t^2y^{''}+7ty^'+9y=0 is y=(c_{1})/(t^3)+(c_{2}ln(t))/(t^3)

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t^2y^{''}+7ty^'+9y=0

t^{2} y^{^{''}} + 7 t y^{^{'}} + 9 y = 0

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

Solution steps

t^{2} y^{''} (t) + 7 t y^{'} (t) + 9 y = 0

Solve linear ODE:

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

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

\int \frac{x ^{5}}{( x ^{3} + 1 ) ^{2}} d x

x \to 1 lim (cos (\frac{π}{2} x))

\frac{d}{d x} ((x - 5)^{\frac{2}{3}})

\frac{d}{d x} (arcsin (- 3 x))

y^{^{''}} = - 4 y - 4 y^{^{'}}

What is the solution for t^2y^{''}+7ty^'+9y=0 ?
The solution for t^2y^{''}+7ty^'+9y=0 is y=(c_{1})/(t^3)+(c_{2}ln(t))/(t^3)