(d^2)/(dt^2)(θ(t))+4*θ(t)=csc^2(2t)

解

\frac{d ^{2} θ}{d t ^{2}} + 4 \cdot θ = csc^{2} (2 t)

θ = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{1}{4} ln (tan (t)) cos (2 t) + \frac{1}{8} sin (2 t) (- cot (t) - tan (t))

解答ステップ

\frac{d ^{2} θ}{d t ^{2}} + 4 \cdot θ = csc^{2} (2 t)

線形 ODE を解く:

θ = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{1}{4} ln (tan (t)) cos (2 t) + \frac{1}{8} sin (2 t) (- cot (t) - tan (t))

θ = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{1}{4} ln (tan (t)) cos (2 t) + \frac{1}{8} sin (2 t) (- cot (t) - tan (t))