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

Lösung

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

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

Schritte zur Lösung

y^{'''} (x) + y^{''} (x) = 3 e^{- x} + x

Solve linear ODE:

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

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

y^{^{''}} + 25 y = 9 sec (5 x)

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = e^{2 x}

y^{^{''}} + 9 y = g (t), y (0) = 2, y^{^{'}} (0) = 0

4 y^{^{''}} - 6 y^{^{'}} + 2 y = 24 e^{- x} - 10 sin (x)

10 y^{^{''}} + 60 y^{^{'}} + 50 y = 5 e^{- x}