y^{'''}-3y^{''}+3y^'=x-8e^x

Lösung

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} = x - 8 e^{x}

y = c_{1} + e^{\frac{3 x}{2}} (c_{2} cos (\frac{3 x}{2}) + c_{3} sin (\frac{3 x}{2})) + \frac{x ^{2}}{6} + \frac{x}{3} - 8 e^{x}

Schritte zur Lösung

y^{'''} (x) - 3 y^{''} (x) + 3 y^{'} (x) = x - 8 e^{x}

Solve linear ODE:

y = c_{1} + e^{\frac{3 x}{2}} (c_{2} cos (\frac{3 x}{2}) + c_{3} sin (\frac{3 x}{2})) + \frac{x ^{2}}{6} + \frac{x}{3} - 8 e^{x}

y = c_{1} + e^{\frac{3 x}{2}} (c_{2} cos (\frac{3 x}{2}) + c_{3} sin (\frac{3 x}{2})) + \frac{x ^{2}}{6} + \frac{x}{3} - 8 e^{x}

y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} + 16 y = 9 - e^{x} + e^{4 x}

y^{^{''}} + y = t^{2} + 2

(d^{2} - 1) y = e^{x} + 4 e^{- x}

y^{^{''}} - 4 y - 12 y = 2 sin (t)

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