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

Lösung

(d^{4} - 1) \cdot 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}

Schritte zur Lösung

(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^{3} - d^{2} + d - 1) y = 4 sin (x)

(d^{2} - 2 d - 3) y = 5

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

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

y^{^{'''}} - 3 y^{^{''}} + 4 y^{^{'}} - 2 y = e^{x}