What is the solution for (d^2-d-2)y=2log_{10}(x)+1/x+1/(x^2) ?

The solution for (d^2-d-2)y=2log_{10}(x)+1/x+1/(x^2) is

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(d^2-d-2)y=2log_{10}(x)+1/x+1/(x^2)

(d^{2} - d - 2) y = 2 lo g_{10} (x) + \frac{1}{x} + \frac{1}{x ^{2}}

y = c_{1} e^{2 x} + c_{2} e^{- x} + e^{2 x} \cdot \int \frac{2 x ^{2} lo g _{10} ( x ) + x + 1}{3 e ^{2 x} x ^{2}} d x - \frac{1}{3} e^{- x} (\frac{( - 2 + 2 ln ( 10 ) ) Ei ( x )}{ln ( 10 )} + 2 e^{x} lo g_{10} (x) - \frac{e ^{x}}{x})

Solution steps

(d^{2} - d - 2) y = 2 lo g_{10} (x) + \frac{1}{x} + \frac{1}{x ^{2}}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} + e^{2 x} \cdot \int \frac{2 x ^{2} lo g _{10} ( x ) + x + 1}{3 e ^{2 x} x ^{2}} d x - \frac{1}{3} e^{- x} (\frac{( - 2 + 2 ln ( 10 ) ) Ei ( x )}{ln ( 10 )} + 2 e^{x} lo g_{10} (x) - \frac{e ^{x}}{x})

y = c_{1} e^{2 x} + c_{2} e^{- x} + e^{2 x} \cdot \int \frac{2 x ^{2} lo g _{10} ( x ) + x + 1}{3 e ^{2 x} x ^{2}} d x - \frac{1}{3} e^{- x} (\frac{( - 2 + 2 ln ( 10 ) ) Ei ( x )}{ln ( 10 )} + 2 e^{x} lo g_{10} (x) - \frac{e ^{x}}{x})

y^{^{''}} - y = x^{2} \cdot e^{x} + 5

y^{^{''}} + 5 y^{^{'}} + 6 y = 5 sin (x)

y^{^{''}} - 4 y^{^{'}} + 3 y = 4 e^{3} x

(d^{4} - 1) y = e^{x} cos (x)

(d^{2} + 1) y = sec (x) + tan (x)

What is the solution for (d^2-d-2)y=2log_{10}(x)+1/x+1/(x^2) ?
The solution for (d^2-d-2)y=2log_{10}(x)+1/x+1/(x^2) is