y^{''}+y^'-12y=2cos(t),y(0)=1,y^'(0)=1

Lösung

y^{^{''}} + y^{^{'}} - 12 y = 2 cos (t), y (0) = 1, y^{^{'}} (0) = 1

y = (- \frac{6}{17} + \frac{98}{85}) e^{3 t} + \frac{6}{17} e^{- 4 t} + \frac{1}{85} sin (t) - \frac{13}{85} cos (t)

Schritte zur Lösung

y^{''} (t) + y^{'} (t) - 12 y = 2 cos (t)

Solve linear ODE:

y = (- \frac{6}{17} + \frac{98}{85}) e^{3 t} + \frac{6}{17} e^{- 4 t} + \frac{1}{85} sin (t) - \frac{13}{85} cos (t)

y = (- \frac{6}{17} + \frac{98}{85}) e^{3 t} + \frac{6}{17} e^{- 4 t} + \frac{1}{85} sin (t) - \frac{13}{85} cos (t)

y^{^{'''}} + 8 y = 2 x - 5 + 8 e^{- 2 x}

y^{^{''}} - y = cosh (t)

y^{^{''}} + 4 y = 4 t^{2} - 4 t + 10, y (0) = 0, y^{^{'}} (0) = 3

y^{^{'''}} - 16 y^{^{'}} = t e^{4 t}

y^{^{''}} + 4 y = 8 t