y^{''}+4y=2csc^2(2x)

Lösung

y^{^{''}} + 4 y = 2 csc^{2} (2 x)

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

Schritte zur Lösung

y^{''} (x) + 4 y = 2 csc^{2} (2 x)

Solve linear ODE:

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

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

2 y^{^{'''}} - 5 y^{^{''}} + 3 y = 3 x^{2} e^{2 x}

y^{^{''}} - 2 y^{^{'}} = 3 x^{2} + 1

(D^{2} + 100) (D^{2} - 100) (D + 10)^{4} x = 100

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

y^{^{''}} + 4 y = x^{2} + 5 \cdot cos (2 x)