What is the solution for y^{''}x^2-5xy^'+9y=0 ?

The solution for y^{''}x^2-5xy^'+9y=0 is y=c_{1}x^3+c_{2}ln(x)x^3

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y^{''}x^2-5xy^'+9y=0

y^{^{''}} x^{2} - 5 x y^{^{'}} + 9 y = 0

y = c_{1} x^{3} + c_{2} ln (x) x^{3}

Solution steps

y^{''} (x) x^{2} - 5 x y^{'} (x) + 9 y = 0

Solve linear ODE:

y = c_{1} x^{3} + c_{2} ln (x) x^{3}

y = c_{1} x^{3} + c_{2} ln (x) x^{3}

cos^{2} (k t)

\int_{0}^{3} 3 d x

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

\int x ln (3) d x

x \to 1 + lim (\frac{2 - x}{x - 1})

What is the solution for y^{''}x^2-5xy^'+9y=0 ?
The solution for y^{''}x^2-5xy^'+9y=0 is y=c_{1}x^3+c_{2}ln(x)x^3