y^{'''}-y^{''}+y^'-y=xe^x-e^{-x}+7

Lösung

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

y = c_{1} e^{x} + c_{2} cos (x) + c_{3} sin (x) + \frac{e ^{x} x ^{2}}{4} - \frac{e ^{x} x}{2} + \frac{1}{4} e^{- x} - 7

Schritte zur Lösung

y^{'''} (x) - y^{''} (x) + y^{'} (x) - y = x e^{x} - e^{- x} + 7

Solve linear ODE:

y = c_{1} e^{x} + c_{2} cos (x) + c_{3} sin (x) + \frac{e ^{x} x ^{2}}{4} - \frac{e ^{x} x}{2} + \frac{1}{4} e^{- x} - 7

y = c_{1} e^{x} + c_{2} cos (x) + c_{3} sin (x) + \frac{e ^{x} x ^{2}}{4} - \frac{e ^{x} x}{2} + \frac{1}{4} e^{- x} - 7

y^{^{''}} + 36 y = csc (6 x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 x + 1

y^{^{''}} - 2 y^{^{'}} = 12 x^{2}

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

y^{^{''}} - 3 y^{^{'}} - 5 = e^{2 x} - 3 cos (3 x)