(D^2+4)y=sinh(x)sin(2x)

Lösung

(D^{2} + 4) y = sinh (x) sin (2 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (2 x) \cdot \int - \frac{sin ^{2} ( 2 x ) sinh ( x )}{2} d x + \frac{1}{68} sin (2 x) (- 4 sinh (x) cos (4 x) + cosh (x) sin (4 x))

Schritte zur Lösung

(D^{2} + 4) y = sinh (x) sin (2 x)

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (2 x) \cdot \int - \frac{sin ^{2} ( 2 x ) sinh ( x )}{2} d x + \frac{1}{68} sin (2 x) (- 4 sinh (x) cos (4 x) + cosh (x) sin (4 x))

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (2 x) \cdot \int - \frac{sin ^{2} ( 2 x ) sinh ( x )}{2} d x + \frac{1}{68} sin (2 x) (- 4 sinh (x) cos (4 x) + cosh (x) sin (4 x))

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

y^{^{'''}} - 24 y^{^{''}} + 2048 y = e^{16 x}

y^{^{''}} + y = sec (2) [t]

y^{^{''}} + 2 y^{^{'}} - 2 y = t^{2}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 3 \cdot y^{^{'}} + 2 y = sin (e^{x})