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

Lösung

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

y = c_{1} e^{- x} + c_{2} cos (x) + c_{3} sin (x) + \frac{e ^{- x} x}{2} + 4 x - 4

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} cos (x) + c_{3} sin (x) + \frac{e ^{- x} x}{2} + 4 x - 4

y = c_{1} e^{- x} + c_{2} cos (x) + c_{3} sin (x) + \frac{e ^{- x} x}{2} + 4 x - 4

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}

x^{^{''}} + 2 x^{^{'}} + 7 x = 6 cos (2 t)