What is the solution for (d-1)^2*y=e^x*sec^2(x)tan(x) ?

The solution for (d-1)^2*y=e^x*sec^2(x)tan(x) is y=c_{1}e^x+c_{2}xe^x+(-e^xx+e^xtan(x))/2

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(d-1)^2y=e^xsec^2(x)tan(x)

(d - 1)^{2} \cdot y = e^{x} \cdot sec^{2} (x) tan (x)

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{- e ^{x} x + e ^{x} tan ( x )}{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{- e ^{x} x + e ^{x} tan ( x )}{2}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{- e ^{x} x + e ^{x} tan ( x )}{2}

y^{^{''}} + y^{^{'}} - 2 y = 20 sin (2 x)

(d^{2} + 3 d + 2) y = sin (e^{x})

(d^{3} + 8) y = x^{4} + x + 1

(d^{2} + d + 1) y = x^{3}

(d^{2} - 4 d + 4) y = x^{3}

What is the solution for (d-1)^2*y=e^x*sec^2(x)tan(x) ?
The solution for (d-1)^2*y=e^x*sec^2(x)tan(x) is y=c_{1}e^x+c_{2}xe^x+(-e^xx+e^xtan(x))/2