y^{''}+3y^'+7y=cos(t),y(0)=0,y^'(0)=2

Lösung

y^{^{''}} + 3 y^{^{'}} + 7 y = cos (t), y (0) = 0, y^{^{'}} (0) = 2

y = e^{- \frac{3 t}{2}} (- \frac{2}{15} cos (\frac{19 t}{2}) + \frac{52}{15 19} sin (\frac{19 t}{2})) + \frac{1}{15} sin (t) + \frac{2}{15} cos (t)

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- \frac{3 t}{2}} (- \frac{2}{15} cos (\frac{19 t}{2}) + \frac{52}{15 19} sin (\frac{19 t}{2})) + \frac{1}{15} sin (t) + \frac{2}{15} cos (t)

y = e^{- \frac{3 t}{2}} (- \frac{2}{15} cos (\frac{19 t}{2}) + \frac{52}{15 19} sin (\frac{19 t}{2})) + \frac{1}{15} sin (t) + \frac{2}{15} cos (t)

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y (0) = 0, y (0) = 0

4 y^{^{''}} + 4 y^{^{'}} + 1 = 0

D (x) = a - 2

(D^{3} + 1) y = 3 + e^{- x} + 5 e^{2 x}

y^{^{''}} + 4 y = 9 t, y (0) = 0, y (0) = 7