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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 x + 3

y^{^{''}} + 6 y^{^{'}} + 5 y = - 9 e^{2 x}

y^{^{''}} + 18 y^{^{'}} + 81 y = x, y (0) = 0, y^{^{'}} (0) = 0

20 y^{^{''}} + 9 y^{^{'}} + x = 0, y (0) = 0, y^{^{'}} (0) = 3

so l v e f or d, d (x) = \frac{2 x ^{3} + 1}{x ^{6}}