What is the solution for x^2y^{''}-7xy^'+12y=0 ?

The solution for x^2y^{''}-7xy^'+12y=0 is y=c_{1}x^6+c_{2}x^2

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x^2y^{''}-7xy^'+12y=0

x^{2} y^{^{''}} - 7 x y^{^{'}} + 12 y = 0

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

Solution steps

x^{2} y^{''} (x) - 7 x y^{'} (x) + 12 y = 0

Solve linear ODE:

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

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

\int \frac{x}{cos ^{2} ( x ^{2} )} d x

\int x^{2} sin (x z) d z

x \to 0 lim (\frac{x + 2 - 2}{2 x + 5 - 3})

\int cos (x) \cdot sin^{3} (x) d x

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

What is the solution for x^2y^{''}-7xy^'+12y=0 ?
The solution for x^2y^{''}-7xy^'+12y=0 is y=c_{1}x^6+c_{2}x^2