y^{'''}-y^'=t

Lösung

y^{^{'''}} - y^{^{'}} = t

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

Schritte zur Lösung

y^{'''} (t) - y^{'} (t) = t

Solve linear ODE:

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

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

y^{^{''}} - y = 1 + e^{x}

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

(D^{2} - 1) y = 2 \cdot (1 + e^{x})^{- 1}

y^{^{''}} - 10 y^{^{'}} + 25 y = 2 e^{5 x}

y^{^{''}} + 9 y^{^{'}} + 20 = 0