What is the solution for x^2y^{''}-16xy^'+72y=0 ?

The solution for x^2y^{''}-16xy^'+72y=0 is y=c_{1}x^9+c_{2}x^8

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x^2y^{''}-16xy^'+72y=0

x^{2} y^{^{''}} - 16 x y^{^{'}} + 72 y = 0

y = c_{1} x^{9} + c_{2} x^{8}

Solution steps

x^{2} y^{''} (x) - 16 x y^{'} (x) + 72 y = 0

Solve linear ODE:

y = c_{1} x^{9} + c_{2} x^{8}

y = c_{1} x^{9} + c_{2} x^{8}

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

f (x) = 6 x - x^{2}

\int \frac{1}{5 - 5 x} d x

y^{^{'}} + y^{3} x + y = 0

\int cos (2 u) d u

What is the solution for x^2y^{''}-16xy^'+72y=0 ?
The solution for x^2y^{''}-16xy^'+72y=0 is y=c_{1}x^9+c_{2}x^8