y^{''''}+36y^{''}=sin(6t)+te^{7t}+4

Lösung

y^{^{''''}} + 36 y^{^{''}} = sin (6 t) + t e^{7 t} + 4

y = c_{1} + c_{2} t + c_{3} cos (6 t) + c_{4} sin (6 t) + \frac{t cos ( 6 t )}{432} + \frac{e ^{7 t} t}{4165} - \frac{268}{2478175} e^{7 t} + \frac{t ^{2}}{18}

Schritte zur Lösung

y^{(4)} (t) + 36 y^{''} (t) = sin (6 t) + t e^{7 t} + 4

Solve linear ODE:

y = c_{1} + c_{2} t + c_{3} cos (6 t) + c_{4} sin (6 t) + \frac{t cos ( 6 t )}{432} + \frac{e ^{7 t} t}{4165} - \frac{268}{2478175} e^{7 t} + \frac{t ^{2}}{18}

y = c_{1} + c_{2} t + c_{3} cos (6 t) + c_{4} sin (6 t) + \frac{t cos ( 6 t )}{432} + \frac{e ^{7 t} t}{4165} - \frac{268}{2478175} e^{7 t} + \frac{t ^{2}}{18}

y^{^{''}} + 8 y = 16 sin (x)

y^{^{''}} - y^{^{'}} - 2 y = 3 e^{2 x} - x^{2}

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

y^{^{''}} + 4 y^{^{'}} + 8 y = sin (x)

y^{^{''}} + 2 y^{^{'}} + 5 y = 12 cos (2 x) + 3 sin (2 x)