What is the solution for x^2(d^2y)/(dx^2)-5xy^'+8y=4x^2 ?

The solution for x^2(d^2y)/(dx^2)-5xy^'+8y=4x^2 is y=c_{1}x^4+c_{2}x^2-x^2-2x^2ln(x)

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x^2(d^2y)/(dx^2)-5xy^'+8y=4x^2

x^{2} \frac{d ^{2} y}{d x ^{2}} - 5 x y^{^{'}} + 8 y = 4 x^{2}

y = c_{1} x^{4} + c_{2} x^{2} - x^{2} - 2 x^{2} ln (x)

Solution steps

x^{2} y^{''} (x) - 5 x y^{'} (x) + 8 y = 4 x^{2}

Solve linear ODE:

y = c_{1} x^{4} + c_{2} x^{2} - x^{2} - 2 x^{2} ln (x)

y = c_{1} x^{4} + c_{2} x^{2} - x^{2} - 2 x^{2} ln (x)

\int_{0}^{1} 2 π (x + 1) (x^{2}) d x

y = (3)^{x}, at x = 6

\int \frac{1}{( x + 5 ) ^{2} ( x - 4 )} d x

- 3 t

\frac{d}{d x} (6 sin (sin (x)))

What is the solution for x^2(d^2y)/(dx^2)-5xy^'+8y=4x^2 ?
The solution for x^2(d^2y)/(dx^2)-5xy^'+8y=4x^2 is y=c_{1}x^4+c_{2}x^2-x^2-2x^2ln(x)