y^{'''}-3y^{''}+3y^'-y=x-8ex

Lösung

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 8 e x

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + (- 1 + 8 e) x + 3 (- 1 + 8 e)

Schritte zur Lösung

y^{'''} (x) - 3 y^{''} (x) + 3 y^{'} (x) - y = x - 8 e x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + (- 1 + 8 e) x + 3 (- 1 + 8 e)

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + (- 1 + 8 e) x + 3 (- 1 + 8 e)

y^{^{''}} - 36 y^{^{'}} = - 42 e^{- 5 t}, y (0) = 7, y^{^{'}} (0) = 0

2 \frac{d ^{2} y}{d t ^{2}} + 20 \frac{d y}{d t} + 50 = 8 \cdot (t)

y^{^{''}} - y = 2^{x}

x^{^{''}} - 3 x^{^{'}} + 2 x = 2 sin (t) - 6 cos (t)

y^{^{''}} - 7 y^{^{'}} + 12 y = 6 e^{x}