What is the solution for x^2y^{''}+xy^'+9y=0,y(1)=0,y^'(1)=2.5 ?

The solution for x^2y^{''}+xy^'+9y=0,y(1)=0,y^'(1)=2.5 is y=0.83333…sin(3ln(x))

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x^2y^{''}+xy^'+9y=0,y(1)=0,y^'(1)=2.5

x^{2} y^{^{''}} + x y^{^{'}} + 9 y = 0, y (1) = 0, y^{^{'}} (1) = 2.5

y = 0.83333 \dots sin (3 ln (x))

Solution steps

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

Solve linear ODE:

y = 0.83333 \dots sin (3 ln (x))

y = 0.83333 \dots sin (3 ln (x))

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\int \frac{1}{( 4 y ) ^{2}} d y

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(0, - 2), (3, 0)

\frac{e ^{1 - s}}{1 - s}

What is the solution for x^2y^{''}+xy^'+9y=0,y(1)=0,y^'(1)=2.5 ?
The solution for x^2y^{''}+xy^'+9y=0,y(1)=0,y^'(1)=2.5 is y=0.83333…sin(3ln(x))