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

Lösung

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

y = c_{1} e^{- 2 x} + c_{2} e^{- 8 x} + 7 sin (3 x) - 30 cos (3 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 8 x} + 7 sin (3 x) - 30 cos (3 x)

y = c_{1} e^{- 2 x} + c_{2} e^{- 8 x} + 7 sin (3 x) - 30 cos (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

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