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

The solution for x^2y^{''}-6y=0,y(1)=6,y^'(1)=-2 is y=2x^3+4/(x^2)

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

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

y = 2 x^{3} + \frac{4}{x ^{2}}

Solution steps

x^{2} y^{''} (x) - 6 y = 0

Solve linear ODE:

y = 2 x^{3} + \frac{4}{x ^{2}}

y = 2 x^{3} + \frac{4}{x ^{2}}

\frac{\partial}{\partial x} (e^{x y} y^{2} + \frac{x}{y})

\int e^{- \frac{x ^{2}}{2}} d x

\int_{0}^{1} \frac{x ^{4} + 3}{x} d x

y = \frac{1}{( 3 x + 8 ) ^{2}}

x \to - 3 lim (5 x)

What is the solution for x^2y^{''}-6y=0,y(1)=6,y^'(1)=-2 ?
The solution for x^2y^{''}-6y=0,y(1)=6,y^'(1)=-2 is y=2x^3+4/(x^2)