(d^2)/(dt^2)(θ(t))+4θ(t)=cos^2(2t)

解

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

θ = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{cos ^{4} ( 2 t ) + sin ( 2 t ) ( 3 sin ( 2 t ) - sin ^{3} ( 2 t ) )}{12}

解答ステップ

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

線形 ODE を解く:

θ = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{cos ^{4} ( 2 t ) + sin ( 2 t ) ( 3 sin ( 2 t ) - sin ^{3} ( 2 t ) )}{12}

θ = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{cos ^{4} ( 2 t ) + sin ( 2 t ) ( 3 sin ( 2 t ) - sin ^{3} ( 2 t ) )}{12}