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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

(D - 1) y = 2 sin (5 t), y (0) = 0

x^{^{''}} - 3 x^{^{'}} + x = - e^{t}

y^{^{''}} - 4 y^{^{'}} = 1

y^{^{''}} + 5 y = e^{2 x} - x - x^{2} + x^{3}

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 6 e^{x}