x^{''}+5x^'+17x=12cos(3t)

Lösung

x^{^{''}} + 5 x^{^{'}} + 17 x = 12 cos (3 t)

x = e^{- \frac{5 t}{2}} (c_{1} cos (\frac{43 t}{2}) + c_{2} sin (\frac{43 t}{2})) + \frac{180}{289} sin (3 t) + \frac{96}{289} cos (3 t)

Schritte zur Lösung

x^{''} (t) + 5 x^{'} (t) + 17 x = 12 cos (3 t)

Solve linear ODE:

x = e^{- \frac{5 t}{2}} (c_{1} cos (\frac{43 t}{2}) + c_{2} sin (\frac{43 t}{2})) + \frac{180}{289} sin (3 t) + \frac{96}{289} cos (3 t)

x = e^{- \frac{5 t}{2}} (c_{1} cos (\frac{43 t}{2}) + c_{2} sin (\frac{43 t}{2})) + \frac{180}{289} sin (3 t) + \frac{96}{289} cos (3 t)

y^{^{''}} + 2 y^{^{'}} + y = e^{- x} (2 x + 5)

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

y^{^{''}} - 8 y^{^{'}} + 16 y = 16 e^{4 x}

\frac{d ^{3} y}{d x ^{3}} + y = 3 + e^{- x} + 5 e^{2 x}

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