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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} - 8 y^{^{'}} + 16 y = 2 e^{4 x} + 3 cos (4 x) - 2 x + 1

x^{^{''}} - 6 x^{^{'}} + 9 x = 5 t e^{3 t}

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

y^{^{''}} - 3 y^{^{'}} + 7 y = t^{2} + cos (t)

y^{^{'''}} - y^{^{''}} - 9 y^{^{'}} + 9 y = 2 - e^{x} + e^{3 x}