What is the solution for x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0 ?

The solution for x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0 is y=c_{1}cos(ln(x))+c_{2}sin(ln(x))

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x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0

x^{2} \frac{d ^{2} y}{d x ^{2}} + x \frac{d y}{d x} + y = 0

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

Solution steps

x^{2} \frac{d ^{2} y}{d x ^{2}} + x \frac{d y}{d 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))

f (x) = e^{t a n (x)}

\frac{d}{d x} (1 - (x^{2} + y^{2})^{\frac{1}{3}})

\int 4 x - 3 - x^{2} d x

\frac{\partial}{\partial x} (\frac{1}{x yz})

f (x) = - 8 x^{2} + 7 x

What is the solution for x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0 ?
The solution for x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0 is y=c_{1}cos(ln(x))+c_{2}sin(ln(x))