y^{''}+4y=sin(t)-\H(t-2pi)sin(t-2pi)

Lösung

y^{^{''}} + 4 y = sin (t) - H (t - 2 π) sin (t - 2 π)

y = c_{1} cos (2 t) + c_{2} sin (2 t) + cos (2 t) \cdot \int - \frac{sin ( 2 t ) ( sin ( t ) - H ( t - 2 π ) sin ( t - 2 π ) )}{2} d t + sin (2 t) \cdot \int \frac{cos ( 2 t ) ( sin ( t ) - H ( t - 2 π ) sin ( t - 2 π ) )}{2} d t

Schritte zur Lösung

y^{''} (t) + 4 y = sin (t) - H (t - 2 π) sin (t - 2 π)

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + cos (2 t) \cdot \int - \frac{sin ( 2 t ) ( sin ( t ) - H ( t - 2 π ) sin ( t - 2 π ) )}{2} d t + sin (2 t) \cdot \int \frac{cos ( 2 t ) ( sin ( t ) - H ( t - 2 π ) sin ( t - 2 π ) )}{2} d t

y = c_{1} cos (2 t) + c_{2} sin (2 t) + cos (2 t) \cdot \int - \frac{sin ( 2 t ) ( sin ( t ) - H ( t - 2 π ) sin ( t - 2 π ) )}{2} d t + sin (2 t) \cdot \int \frac{cos ( 2 t ) ( sin ( t ) - H ( t - 2 π ) sin ( t - 2 π ) )}{2} d t

y^{^{''}} + y = sin (a t)

y^{^{''}} - 4 y^{^{'}} + 13 y = 24 e^{2 x} cos (3 x)

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

y^{^{''}} + 5 y^{^{'}} + 4 y = t e^{- t} H (t)

(D^{4} - 2 D^{2} + 1) Y = cos (x)