What is the solution for x^2y^{''}-3xy^'-2y=0 ?

The solution for x^2y^{''}-3xy^'-2y=0 is y=c_{1}x^{2+sqrt(6)}+c_{2}x^{2-sqrt(6)}

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x^2y^{''}-3xy^'-2y=0

x^{2} y^{^{''}} - 3 x y^{^{'}} - 2 y = 0

y = c_{1} x^{2 + 6} + c_{2} x^{2 - 6}

Solution steps

x^{2} y^{''} (x) - 3 x y^{'} (x) - 2 y = 0

Solve linear ODE:

y = c_{1} x^{2 + 6} + c_{2} x^{2 - 6}

y = c_{1} x^{2 + 6} + c_{2} x^{2 - 6}

x \to - \frac{π}{3} lim (- sec (x))

\int (x (x + 1)^{3}) d x

(3 x^{4} - x + 1) (- x^{5} + 4)

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

f (t) = sin (2 t)

What is the solution for x^2y^{''}-3xy^'-2y=0 ?
The solution for x^2y^{''}-3xy^'-2y=0 is y=c_{1}x^{2+sqrt(6)}+c_{2}x^{2-sqrt(6)}