What is the solution for x^2y^{''}+5xy^'+3y=0 ?

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

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x^2y^{''}+5xy^'+3y=0

x^{2} y^{^{''}} + 5 x y^{^{'}} + 3 y = 0

y = \frac{c _{1}}{x} + \frac{c _{2}}{x ^{3}}

Solution steps

x^{2} y^{''} (x) + 5 x y^{'} (x) + 3 y = 0

Solve linear ODE:

y = \frac{c _{1}}{x} + \frac{c _{2}}{x ^{3}}

y = \frac{c _{1}}{x} + \frac{c _{2}}{x ^{3}}

\frac{d}{d x} (x^{8 x})

x \to 0 lim (- arctan (\frac{x}{2}))

f^{^{'}} (x) = - 4 x^{3} + 2 x^{2} - 7

f (x) = x + 2 cos (x), at x = 0

y = 3 x^{3} - 2 x, (- 1, - 1)

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