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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

t an g e n t 4 x^{3} - 4 x

\frac{d}{d x} (x^{2} - 8 ln (x))

x \to 0 - lim (\frac{x ^{2}}{x})

d er i v a t i v e y = (4 x - 1)^{3}

t an g e n t y = 7 x - x^{2}, at x = 1

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