What is the solution for x^2y^{''}-14xy^'+56y=0 ?

The solution for x^2y^{''}-14xy^'+56y=0 is y=c_{1}x^8+c_{2}x^7

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x^2y^{''}-14xy^'+56y=0

x^{2} y^{^{''}} - 14 x y^{^{'}} + 56 y = 0

y = c_{1} x^{8} + c_{2} x^{7}

Solution steps

x^{2} y^{''} (x) - 14 x y^{'} (x) + 56 y = 0

Solve linear ODE:

y = c_{1} x^{8} + c_{2} x^{7}

y = c_{1} x^{8} + c_{2} x^{7}

\frac{d y}{d x} = e^{y} (2 x^{3} - 4 x)

\int (\frac{x ^{3} + 2 x ^{2} - 4}{x ^{2}}) d x

\int_{1}^{2} x - 1 d x

\frac{3 s}{( s ^{2} + 4 )}

y^{^{''''}} + 2 y^{^{''}} + y = 0

What is the solution for x^2y^{''}-14xy^'+56y=0 ?
The solution for x^2y^{''}-14xy^'+56y=0 is y=c_{1}x^8+c_{2}x^7