(d^2)/(dx^2)(θ(x))+4θ(x)=csc^2(2x)

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

(D^{4} + D^{2}) y = 3 x^{2} + 4 sin (x) - 2 cos (x)

y^{^{''}} + 2 y = - 18 x e^{2 x}

y^{^{''}} - y^{^{'}} - 6 y = 2 cos (x) - 2 e^{3 x} + 10

y^{^{''}} + 5 y^{^{'}} + 6 y = x e^{- 2 x}

\frac{d ^{2} x}{d t ^{2}} + 7 \frac{d x}{d t} + 6 x = 5 e^{- t}