What is the solution for x^2y^{''}+17xy^'+145y=0 ?

The solution for x^2y^{''}+17xy^'+145y=0 is y=(c_{1}cos(9ln(x))+c_{2}sin(9ln(x)))/(x^8)

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x^2y^{''}+17xy^'+145y=0

x^{2} y^{^{''}} + 17 x y^{^{'}} + 145 y = 0

y = \frac{c _{1} cos ( 9 ln ( x ) ) + c _{2} sin ( 9 ln ( x ) )}{x ^{8}}

Solution steps

x^{2} y^{''} (x) + 17 x y^{'} (x) + 145 y = 0

Solve linear ODE:

y = \frac{c _{1} cos ( 9 ln ( x ) ) + c _{2} sin ( 9 ln ( x ) )}{x ^{8}}

y = \frac{c _{1} cos ( 9 ln ( x ) ) + c _{2} sin ( 9 ln ( x ) )}{x ^{8}}

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What is the solution for x^2y^{''}+17xy^'+145y=0 ?
The solution for x^2y^{''}+17xy^'+145y=0 is y=(c_{1}cos(9ln(x))+c_{2}sin(9ln(x)))/(x^8)