What is the solution for (d^4-1)y=sin(x) ?

The solution for (d^4-1)y=sin(x) is y=c_{1}e^x+c_{2}e^{-x}+c_{3}cos(x)+c_{4}sin(x)+(xcos(x))/4

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(d^4-1)y=sin(x)

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

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} cos (x) + c_{4} sin (x) + \frac{x cos ( x )}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} cos (x) + c_{4} sin (x) + \frac{x cos ( x )}{4}

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} cos (x) + c_{4} sin (x) + \frac{x cos ( x )}{4}

(d^{2} + 4 d - 12) y = (x - 1) e^{2} x

(d - 2)^{2} \cdot y = x^{2} - lo g_{10} (2)

(d^{2} - 3 d + 2) y = x \cdot e^{x}

y^{^{''}} - 4 y^{^{'}} + 4 y = 12 e^{2 x} + x^{2}

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

What is the solution for (d^4-1)y=sin(x) ?
The solution for (d^4-1)y=sin(x) is y=c_{1}e^x+c_{2}e^{-x}+c_{3}cos(x)+c_{4}sin(x)+(xcos(x))/4