y^{''''}+25y^{''}=sin(5t)+te^{6t}+4

Lösung

y^{^{''''}} + 25 y^{^{''}} = sin (5 t) + t e^{6 t} + 4

y = c_{1} + c_{2} t + c_{3} cos (5 t) + c_{4} sin (5 t) + \frac{t cos ( 5 t )}{250} + \frac{e ^{6 t} t}{2196} - \frac{97}{401868} e^{6 t} + \frac{2 t ^{2}}{25}

Schritte zur Lösung

y^{(4)} (t) + 25 y^{''} (t) = sin (5 t) + t e^{6 t} + 4

Solve linear ODE:

y = c_{1} + c_{2} t + c_{3} cos (5 t) + c_{4} sin (5 t) + \frac{t cos ( 5 t )}{250} + \frac{e ^{6 t} t}{2196} - \frac{97}{401868} e^{6 t} + \frac{2 t ^{2}}{25}

y = c_{1} + c_{2} t + c_{3} cos (5 t) + c_{4} sin (5 t) + \frac{t cos ( 5 t )}{250} + \frac{e ^{6 t} t}{2196} - \frac{97}{401868} e^{6 t} + \frac{2 t ^{2}}{25}

6 y^{^{''}} - 10 y^{^{'}} - 4 y = x + 2

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

y^{^{''}} - y^{^{'}} = x e [x], y (0) = 2, y^{^{'}} (0) = 1

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

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