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

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

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

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

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

Solution steps

x^{2} y^{''} (x) - 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}

x \to 2 lim (x^{2} - 7 x + 5)

\int_{0}^{1} x e^{- 8 x^{2}} d x

\frac{d y}{d x} + 9 y = 3

y^{^{''}} + 2 y = cos (t) - 2 \cdot sin (2 t)

\int 3 e^{- 3 x} d x

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