2x^{''}+4x+20x=20\H(t)

解

2 x^{^{''}} + 4 x + 20 x = 20 H (t)

x = c_{1} cos (23 t) + c_{2} sin (23 t) + cos (23 t) \cdot \int - \frac{5 3 sin ( 2 3 t ) H ( t )}{3} d t + sin (23 t) \cdot \int \frac{5 3 cos ( 2 3 t ) H ( t )}{3} d t

解答ステップ

2 x^{''} (t) + 4 x + 20 x = 20 H (t)

線形 ODE を解く:

x = c_{1} cos (23 t) + c_{2} sin (23 t) + cos (23 t) \cdot \int - \frac{5 3 sin ( 2 3 t ) H ( t )}{3} d t + sin (23 t) \cdot \int \frac{5 3 cos ( 2 3 t ) H ( t )}{3} d t

x = c_{1} cos (23 t) + c_{2} sin (23 t) + cos (23 t) \cdot \int - \frac{5 3 sin ( 2 3 t ) H ( t )}{3} d t + sin (23 t) \cdot \int \frac{5 3 cos ( 2 3 t ) H ( t )}{3} d t