y^{''}-2y^'+y=10cos(x)+8sin(x)

Lösung

y^{^{''}} - 2 y^{^{'}} + y = 10 cos (x) + 8 sin (x)

y = c_{1} e^{x} + c_{2} x e^{x} - 5 sin (x) + 4 cos (x)

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + y = 10 cos (x) + 8 sin (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} - 5 sin (x) + 4 cos (x)

y = c_{1} e^{x} + c_{2} x e^{x} - 5 sin (x) + 4 cos (x)

y^{^{''}} + 10 y^{^{'}} + 16 y = 949 sin (3 x)

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- x} + 4 x

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

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 50, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 4 y = t^{2} + 10 e^{t}, y (0) = 0, y^{^{'}} (0) = 7