What is the solution for x^2y^{''}+15xy^'+49y=0 ?

The solution for x^2y^{''}+15xy^'+49y=0 is y=(c_{1})/(x^7)+(c_{2}ln(x))/(x^7)

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x^2y^{''}+15xy^'+49y=0

x^{2} y^{^{''}} + 15 x y^{^{'}} + 49 y = 0

y = \frac{c _{1}}{x ^{7}} + \frac{c _{2} ln ( x )}{x ^{7}}

Solution steps

x^{2} y^{''} (x) + 15 x y^{'} (x) + 49 y = 0

Solve linear ODE:

y = \frac{c _{1}}{x ^{7}} + \frac{c _{2} ln ( x )}{x ^{7}}

y = \frac{c _{1}}{x ^{7}} + \frac{c _{2} ln ( x )}{x ^{7}}

\frac{1}{s ^{2} + 10.1 s + 1}

\int x - 2 d x

f (x) = 3 x + x^{\frac{4}{3}}

x \to 0 + lim (\frac{1}{x} \cdot e^{\frac{1}{x}})

f (x) = 3 cos (2 x)

What is the solution for x^2y^{''}+15xy^'+49y=0 ?
The solution for x^2y^{''}+15xy^'+49y=0 is y=(c_{1})/(x^7)+(c_{2}ln(x))/(x^7)