(D^2-2D+2)y=3e^xsin(x)

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 9 y = sin (x) - 2

y^{^{'''}} - y^{^{'}} = tan (x)

y^{^{''}} + 4 y^{^{'}} + 8 y = 12 e^{- 2 x} sec (2 x)

y^{^{''}} - 4 y = 20

y^{^{''}} + y = sinh (2 x)