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

Lösung

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

y = c_{1} e^{x} + c_{2} x e^{x} - e^{x} sin (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} - e^{x} sin (x)

y = c_{1} e^{x} + c_{2} x e^{x} - e^{x} sin (x)

y^{^{''}} + 2 y^{^{'}} + y = 21 e^{- t}

y^{^{''}} - 2 y^{^{'}} + y = 8 e^{x} - \frac{1}{6} x^{3} + 3 x

y^{^{''}} + y^{^{'}} = 5

3 y^{^{''}} + 4 y + 2 = 0

y^{^{''}} + 5 y^{^{'}} + 6 y = 2 e^{- t}