x^{''}-4x^'=20cos(5t)-4sin(5t)-7

Lösung

x^{^{''}} - 4 x^{^{'}} = 20 cos (5 t) - 4 sin (5 t) - 7

x = c_{1} e^{4 t} + c_{2} + \frac{7 t}{4} - \frac{12}{41} sin (5 t) - \frac{116}{205} cos (5 t)

Schritte zur Lösung

x^{''} (t) - 4 x^{'} (t) = 20 cos (5 t) - 4 sin (5 t) - 7

Solve linear ODE:

x = c_{1} e^{4 t} + c_{2} + \frac{7 t}{4} - \frac{12}{41} sin (5 t) - \frac{116}{205} cos (5 t)

x = c_{1} e^{4 t} + c_{2} + \frac{7 t}{4} - \frac{12}{41} sin (5 t) - \frac{116}{205} cos (5 t)

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 = 0

(\frac{d ^{2} y}{d x ^{2}} - 9 y) = e^{- 4 x} cos (e^{- x})

y^{^{'''}} + 8 y = 8 \cdot e^{- 2 \cdot t}

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

\frac{d ^{2} y}{d x ^{2}} + 36 y = 288 sin (6 x) + 96 cos (6 x)