What is the solution for y^{''}-6/x y^'+(10)/(x^2)y=0 ?

The solution for y^{''}-6/x y^'+(10)/(x^2)y=0 is y=c_{1}x^5+c_{2}x^2

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y^{''}-6/x y^'+(10)/(x^2)y=0

y^{^{''}} - \frac{6}{x} y^{^{'}} + \frac{10}{x ^{2}} y = 0

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

Solution steps

y^{''} (x) - \frac{6}{x} y^{'} (x) + \frac{10}{x ^{2}} y = 0

Solve linear ODE:

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

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

h \to 0 lim (\frac{h + 5 - 5}{h})

y = \frac{2}{1 - 3 x}, at x = - 1

\int \frac{x + 8}{x ^{2} + 9} d x

\int \frac{1}{x ^{2} - 400} d x

\frac{\partial}{\partial x} (2 x^{8 y})

What is the solution for y^{''}-6/x y^'+(10)/(x^2)y=0 ?
The solution for y^{''}-6/x y^'+(10)/(x^2)y=0 is y=c_{1}x^5+c_{2}x^2