y^{'''}-y^{''}+4y^'-4y=-3e^t+4e^{2t}

Lösung

y^{^{'''}} - y^{^{''}} + 4 y^{^{'}} - 4 y = - 3 e^{t} + 4 e^{2 t}

y = c_{1} e^{t} + c_{2} cos (2 t) + c_{3} sin (2 t) - \frac{3 e ^{t} t}{5} + \frac{1}{2} e^{2 t}

Schritte zur Lösung

y^{'''} (t) - y^{''} (t) + 4 y^{'} (t) - 4 y = - 3 e^{t} + 4 e^{2 t}

Solve linear ODE:

y = c_{1} e^{t} + c_{2} cos (2 t) + c_{3} sin (2 t) - \frac{3 e ^{t} t}{5} + \frac{1}{2} e^{2 t}

y = c_{1} e^{t} + c_{2} cos (2 t) + c_{3} sin (2 t) - \frac{3 e ^{t} t}{5} + \frac{1}{2} e^{2 t}

y^{^{''}} - 8 y^{^{'}} + 16 y = 8 + 16 x

y^{^{''}} + y = 2 x \cdot sin (x)

2 y^{^{''}} - 4 y^{^{'}} + 3 y = 2 e^{3 x} - 6

y^{^{''}} - 5 y = (x - 1) sin (x) + (x + 1) cos (x)

y^{^{''}} + 9 y^{^{'}} + 8 y = 3 e^{5 x}