What is the solution for x^2(d^2y)/(dx^2)+5x(dy)/(dx)-32y=0 ?

The solution for x^2(d^2y)/(dx^2)+5x(dy)/(dx)-32y=0 is y=c_{1}x^4+(c_{2})/(x^8)

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x^2(d^2y)/(dx^2)+5x(dy)/(dx)-32y=0

x^{2} \frac{d ^{2} y}{d x ^{2}} + 5 x \frac{d y}{d x} - 32 y = 0

y = c_{1} x^{4} + \frac{c _{2}}{x ^{8}}

Solution steps

x^{2} \frac{d ^{2} y}{d x ^{2}} + 5 x \frac{d y}{d x} - 32 y = 0

Solve linear ODE:

y = c_{1} x^{4} + \frac{c _{2}}{x ^{8}}

y = c_{1} x^{4} + \frac{c _{2}}{x ^{8}}

x \to \infty lim (\frac{3 x + e ^{- x}}{2 x + e ^{- 2 x}})

\frac{\partial}{\partial x} (\frac{e ^{\frac{x ^{2}}{4 t}} t x}{2})

(10, - 6), (8, - 16)

y = 3 sin (2 x), y = 3 cos (2 x)

\int \frac{1}{x ^{2}} sin (\frac{1}{x}) d x

What is the solution for x^2(d^2y)/(dx^2)+5x(dy)/(dx)-32y=0 ?
The solution for x^2(d^2y)/(dx^2)+5x(dy)/(dx)-32y=0 is y=c_{1}x^4+(c_{2})/(x^8)