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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int 5 sec^{3} (x) d x

\frac{d}{d x} (e^{2 x} sin (2 x))

\frac{d}{d x} (\frac{( x )}{x + 1})

\frac{d}{d x} ((x^{2} + 1) e^{- x})

y = \frac{7 x - 3}{5 x + 4} + x^{3}

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