y^{'''}-y^'=e^t(1+t)

Lösung

y^{^{'''}} - y^{^{'}} = e^{t} (1 + t)

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{2 e ^{t} t ^{2} - 2 e ^{t} t + e ^{t}}{8}

Schritte zur Lösung

y^{'''} (t) - y^{'} (t) = e^{t} (1 + t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{2 e ^{t} t ^{2} - 2 e ^{t} t + e ^{t}}{8}

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{2 e ^{t} t ^{2} - 2 e ^{t} t + e ^{t}}{8}

(d^{2} - 2 d + 5) y = e^{2 x} \cdot sin (x)

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = x^{3} + 2 x^{2} + 5 x + 2

y^{^{''}} + 9 y = 2 x^{2} e^{3 x} + 5

y^{^{''}} - y^{^{'}} - 12 y = - 5 e^{3 x}, y (0) = 0, y^{^{'}} (0) = 0

x^{^{''}} + 16 x^{^{'}} = 144, x (0) = 5, x^{^{'}} (0) = 12