4y^{''}-7y^'+3y=te^{2t}sin(-2t)

Lösung

4 y^{^{''}} - 7 y^{^{'}} + 3 y = t e^{2 t} sin (- 2 t)

y = c_{1} e^{t} + c_{2} e^{\frac{3 t}{4}} + e^{t} \cdot \int - e^{t} t sin (2 t) d t + e^{\frac{3 t}{4}} \cdot \int e^{\frac{5 t}{4}} t sin (2 t) d t

Schritte zur Lösung

4 y^{''} (t) - 7 y^{'} (t) + 3 y = t e^{2 t} sin (- 2 t)

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{\frac{3 t}{4}} + e^{t} \cdot \int - e^{t} t sin (2 t) d t + e^{\frac{3 t}{4}} \cdot \int e^{\frac{5 t}{4}} t sin (2 t) d t

y = c_{1} e^{t} + c_{2} e^{\frac{3 t}{4}} + e^{t} \cdot \int - e^{t} t sin (2 t) d t + e^{\frac{3 t}{4}} \cdot \int e^{\frac{5 t}{4}} t sin (2 t) d t

(D^{2} - 3 D + 2) y = e^{5 x}

y^{^{''''}} - 2 y^{^{'''}} + y^{^{''}} = e^{x + 1}

y^{^{''}} + 3 y^{^{'}} + 6 = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = 1, y^{^{'}} (0) = 0

y^{^{''}} - 10 y^{^{'}} + 21 y = 240 e^{t}