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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + y = 1, y^{^{'}} (0) = - 1

y^{^{''}} + y = 1, y^{^{'}} (0) = - 3

y^{^{''}} + 4 y = t cos (2 t)

y^{^{''}} - 2 y^{^{'}} - 3 y = 5 e^{4} x, y (0) = 1, y^{^{'}} (0) = 0

9 y^{^{''}} + 4 y = 3 x + 12 e^{- x}