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

The solution for x^2y^{''}-4xy^'+6y=0,y(1)=-2,y^'(1)=4 is y=8x^3-10x^2

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x^2y^{''}-4xy^'+6y=0,y(1)=-2,y^'(1)=4

x^{2} y^{^{''}} - 4 x y^{^{'}} + 6 y = 0, y (1) = - 2, y^{^{'}} (1) = 4

y = 8 x^{3} - 10 x^{2}

Solution steps

x^{2} y^{''} (x) - 4 x y^{'} (x) + 6 y = 0

Solve linear ODE:

y = 8 x^{3} - 10 x^{2}

y = 8 x^{3} - 10 x^{2}

\frac{\partial}{\partial x} (3 x^{2} + 2 y^{4})

x \to 0 lim (lo g_{e} (1 + x))

\int sin (x) (1 + sec^{2} (x)) d x

\frac{d x}{d t} = 1.5 t cos^{2} (x), x (0) = - 1.4

f (x) = 4 x - 4 x

What is the solution for x^2y^{''}-4xy^'+6y=0,y(1)=-2,y^'(1)=4 ?
The solution for x^2y^{''}-4xy^'+6y=0,y(1)=-2,y^'(1)=4 is y=8x^3-10x^2