y^{'''}+4y^{''}+3y^'=2+e^2t

Lösung

y^{^{'''}} + 4 y^{^{''}} + 3 y^{^{'}} = 2 + e^{2} t

y = c_{1} + c_{2} e^{- t} + c_{3} e^{- 3 t} + \frac{e ^{2} t ^{2}}{6} + \frac{( 6 - 4 e ^{2} ) t}{9}

Schritte zur Lösung

y^{'''} (t) + 4 y^{''} (t) + 3 y^{'} (t) = 2 + e^{2} t

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + c_{3} e^{- 3 t} + \frac{e ^{2} t ^{2}}{6} + \frac{( 6 - 4 e ^{2} ) t}{9}

y = c_{1} + c_{2} e^{- t} + c_{3} e^{- 3 t} + \frac{e ^{2} t ^{2}}{6} + \frac{( 6 - 4 e ^{2} ) t}{9}

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

y^{^{''}} + y = 3 cos (t), y (0) = 0, y^{^{'}} (0) = 0

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

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 54 + 18

so l v e f or d, d (x) = e^{2 x^{3} + 4}