y^{'''}-y=1

Lösung

y^{^{'''}} - y = 1

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

Schritte zur Lösung

y^{'''} (t) - y = 1

Solve linear ODE:

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

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

y^{^{''}} + 7 y^{^{'}} + 12 y = 4 e^{5 t}, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} - 8 y = 2 e^{4 x} + 3 x e^{2 x} + 4 x

\frac{d ^{2} y}{d t ^{2}} - 2 \frac{d y}{d t} - 15 y = 6 + 4 t

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

y^{^{''}} + 2 y^{^{'}} + 4 y = 111 e^{2 x} cos (3 x)