What is the solution for x^2y^{''}+xy^'+9y=0 ?

The solution for x^2y^{''}+xy^'+9y=0 is y=c_{1}cos(3ln(x))+c_{2}sin(3ln(x))

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x^2y^{''}+xy^'+9y=0

x^{2} y^{^{''}} + x y^{^{'}} + 9 y = 0

y = c_{1} cos (3 ln (x)) + c_{2} sin (3 ln (x))

Solution steps

x^{2} y^{''} (x) + x y^{'} (x) + 9 y = 0

Solve linear ODE:

y = c_{1} cos (3 ln (x)) + c_{2} sin (3 ln (x))

y = c_{1} cos (3 ln (x)) + c_{2} sin (3 ln (x))

\frac{\partial}{\partial x} (y sin (\frac{x}{y}))

f (x) = \frac{x ^{2} - 6 x + 1}{x ^{2} + 4}

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

y^{^{''}} + 6 y + 9 = 0, y (0) = - 3, y^{^{'}} (0) = - 1

\int 4 x^{4} d x

What is the solution for x^2y^{''}+xy^'+9y=0 ?
The solution for x^2y^{''}+xy^'+9y=0 is y=c_{1}cos(3ln(x))+c_{2}sin(3ln(x))