What is the solution for y^{''}-9/x y^'+(34)/(x^2)y=0 ?

The solution for y^{''}-9/x y^'+(34)/(x^2)y=0 is y=x^5(c_{1}cos(3ln(x))+c_{2}sin(3ln(x)))

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y^{''}-9/x y^'+(34)/(x^2)y=0

y^{^{''}} - \frac{9}{x} y^{^{'}} + \frac{34}{x ^{2}} y = 0

y = x^{5} (c_{1} cos (3 ln (x)) + c_{2} sin (3 ln (x)))

Solution steps

y^{''} (x) - \frac{9}{x} y^{'} (x) + \frac{34}{x ^{2}} y = 0

Solve linear ODE:

y = x^{5} (c_{1} cos (3 ln (x)) + c_{2} sin (3 ln (x)))

y = x^{5} (c_{1} cos (3 ln (x)) + c_{2} sin (3 ln (x)))

\frac{d y}{d x} = 5 y + 2

\frac{6 x + 2 x ^{2}}{( 3 + 2 x ) ^{2}}

\int \frac{x + 1}{x ^{2} - 9} d x

\frac{\partial}{\partial x} (- 3 x^{2} y^{3} sin (x^{3} y^{3}))

f (0) = \frac{x}{x ^{2} + 1}

What is the solution for y^{''}-9/x y^'+(34)/(x^2)y=0 ?
The solution for y^{''}-9/x y^'+(34)/(x^2)y=0 is y=x^5(c_{1}cos(3ln(x))+c_{2}sin(3ln(x)))