y^{'''}-4y^'=x+3cos(x)+e^{-2x}

Lösung

y^{^{'''}} - 4 y^{^{'}} = x + 3 cos (x) + e^{- 2 x}

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{- x ^{2} + e ^{- 2 x} x}{8} - \frac{3}{5} sin (x)

Schritte zur Lösung

y^{'''} (x) - 4 y^{'} (x) = x + 3 cos (x) + e^{- 2 x}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{- x ^{2} + e ^{- 2 x} x}{8} - \frac{3}{5} sin (x)

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{- x ^{2} + e ^{- 2 x} x}{8} - \frac{3}{5} sin (x)

y^{^{''}} - 9 y^{^{'}} + 8 y = x

y^{^{''}} + 14 y^{^{'}} + 50 y = 371 cos (t)

y^{^{''}} - 4 y^{^{'}} + 4 y = sin (3 x) e^{2 x}

\frac{d ^{3} x}{d t ^{3}} + x = \frac{1}{2} t^{2} e^{t}

y^{^{''}} - 9 y^{^{'}} + 14 y = 3 x^{2} - 5 sin (2 x) + 7 x e^{6 x}