What is the solution for x^2y^{''}+2xy^'-30y=0,y(1)=-5,y^'(1)=-6 ?

The solution for x^2y^{''}+2xy^'-30y=0,y(1)=-5,y^'(1)=-6 is y=(-5+19/11)x^5-(19)/(11x^6)

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x^2y^{''}+2xy^'-30y=0,y(1)=-5,y^'(1)=-6

x^{2} y^{^{''}} + 2 x y^{^{'}} - 30 y = 0, y (1) = - 5, y^{^{'}} (1) = - 6

y = (- 5 + \frac{19}{11}) x^{5} - \frac{19}{11 x ^{6}}

Solution steps

x^{2} y^{''} (x) + 2 x y^{'} (x) - 30 y = 0

Solve linear ODE:

y = (- 5 + \frac{19}{11}) x^{5} - \frac{19}{11 x ^{6}}

y = (- 5 + \frac{19}{11}) x^{5} - \frac{19}{11 x ^{6}}

y^{^{''}} + 3 y = x

\int t ln (t + 3) d t

\int \frac{1}{b} sin (b x) d x

\int (2 x - 1)^{6} d x

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

What is the solution for x^2y^{''}+2xy^'-30y=0,y(1)=-5,y^'(1)=-6 ?
The solution for x^2y^{''}+2xy^'-30y=0,y(1)=-5,y^'(1)=-6 is y=(-5+19/11)x^5-(19)/(11x^6)