What is the solution for x^2y^{''}-7xy^'+7y=13x^{1/2} ?

The solution for x^2y^{''}-7xy^'+7y=13x^{1/2} is y=c_{1}x^7+c_{2}x+4x^{1/2}

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x^2y^{''}-7xy^'+7y=13x^{1/2}

x^{2} y^{^{''}} - 7 x y^{^{'}} + 7 y = 13 x^{\frac{1}{2}}

y = c_{1} x^{7} + c_{2} x + 4 x^{\frac{1}{2}}

Solution steps

x^{2} y^{''} (x) - 7 x y^{'} (x) + 7 y = 13 x^{\frac{1}{2}}

Solve linear ODE:

y = c_{1} x^{7} + c_{2} x + 4 x^{\frac{1}{2}}

y = c_{1} x^{7} + c_{2} x + 4 x^{\frac{1}{2}}

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

x \to - \infty lim (3^{2 x})

y \frac{d y}{d x} = 3 x y^{2} + 9 x

\int 7 x^{17} e^{- x^{9}} d x

\frac{\partial}{\partial t} (e^{s t})

What is the solution for x^2y^{''}-7xy^'+7y=13x^{1/2} ?
The solution for x^2y^{''}-7xy^'+7y=13x^{1/2} is y=c_{1}x^7+c_{2}x+4x^{1/2}