y^{''}+10y^{''}+33y^'+36y=4te^{-3t}

Lösung

y^{^{''}} + 10 y^{^{''}} + 33 y^{^{'}} + 36 y = 4 t e^{- 3 t}

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{3 5 t}{2 11}) + c_{2} sin (\frac{3 5 t}{2 11})) + \frac{e ^{- 3 t} t}{9} + \frac{11}{108} e^{- 3 t}

Schritte zur Lösung

y^{''} (t) + 10 y^{''} (t) + 33 y^{'} (t) + 36 y = 4 t e^{- 3 t}

Solve linear ODE:

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{3 5 t}{2 11}) + c_{2} sin (\frac{3 5 t}{2 11})) + \frac{e ^{- 3 t} t}{9} + \frac{11}{108} e^{- 3 t}

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{3 5 t}{2 11}) + c_{2} sin (\frac{3 5 t}{2 11})) + \frac{e ^{- 3 t} t}{9} + \frac{11}{108} e^{- 3 t}

y^{^{''}} + 6 y^{^{'}} + 8 y = 16 t + 52

y^{^{''}} - y^{^{'}} - 6 y = 36 x, y (0) = 4, y^{^{'}} (0) = - 17

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

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

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 32 y = 6 + 3 x