What is the solution for 5x^2(d^2y)/(dx^2)-16x(dy)/(dx)+4y=0 ?

The solution for 5x^2(d^2y)/(dx^2)-16x(dy)/(dx)+4y=0 is y=c_{1}x^4+c_{2}\sqrt[5]{x}

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5x^2(d^2y)/(dx^2)-16x(dy)/(dx)+4y=0

5 x^{2} \frac{d ^{2} y}{d x ^{2}} - 16 x \frac{d y}{d x} + 4 y = 0

y = c_{1} x^{4} + c_{2} 5 x

Solution steps

5 x^{2} \frac{d ^{2} y}{d x ^{2}} - 16 x \frac{d y}{d x} + 4 y = 0

Solve linear ODE:

y = c_{1} x^{4} + c_{2} 5 x

y = c_{1} x^{4} + c_{2} 5 x

\int_{0}^{5} x 5 - x d x

x^{2} y^{^{''}} + 2 x y^{^{'}} - 6 y = 0, y (1) = 0

\frac{d}{d x} (e^{5 x + 2 x^{2}})

\frac{d}{d x} (\frac{1}{2} arctan (\frac{x + 1}{2}))

\int sec (t) (sec (t) + tan (t)) d t

What is the solution for 5x^2(d^2y)/(dx^2)-16x(dy)/(dx)+4y=0 ?
The solution for 5x^2(d^2y)/(dx^2)-16x(dy)/(dx)+4y=0 is y=c_{1}x^4+c_{2}\sqrt[5]{x}