(d^2)/(dt^2)(θ(t))+4θ(t)=cos^2(2t)

Lösung

\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}

Schritte zur Lösung

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

Solve linear ODE:

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}

\frac{d ^{3} y}{d x ^{3}} - 12 (\frac{d y}{d x}) + 16 y = 32 x - 8

y^{^{''}} + y^{^{'}} - 6 y = 30 - 30 H (t - 4)

y^{^{''}} + 10 y^{^{'}} + 16 y = 3 cos (5 t) + 4 sin (5 t)

2 y^{^{''}} + 2 y = 2 cos^{2} (x)

y^{^{''}} + 4 y^{^{'}} + 5 y = 35 e^{- 4 x}, y (0) = - 2