y^{''''}+2y^{''}+1=7sin(t)

Lösung

y^{^{''''}} + 2 y^{^{''}} + 1 = 7 sin (t)

y = c_{1} + c_{2} t + c_{3} cos (2 t) + c_{4} sin (2 t) - 7 sin (t) - \frac{t ^{2}}{4}

Schritte zur Lösung

y^{(4)} (t) + 2 y^{''} (t) + 1 = 7 sin (t)

Solve linear ODE:

y = c_{1} + c_{2} t + c_{3} cos (2 t) + c_{4} sin (2 t) - 7 sin (t) - \frac{t ^{2}}{4}

y = c_{1} + c_{2} t + c_{3} cos (2 t) + c_{4} sin (2 t) - 7 sin (t) - \frac{t ^{2}}{4}

(4 d^{2} - 4 d + 1) y = 100

y^{^{''}} - 5 y^{^{'}} + 6 = 0

x^{^{''}} + 2 x^{^{'}} + x = 2 t e^{- t}

y^{^{''}} + y = 2 t

\frac{1}{6} y^{^{''}} + 6 y = tan (6 t) - \frac{1}{2} e^{t}