y^{''}+16y=32sec(2x)

Lösung

y^{^{''}} + 16 y = 32 sec (2 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) + 8 cos (2 x) cos (4 x) + 4 (- ln (tan (2 x) + sec (2 x)) + 2 sin (2 x)) sin (4 x)

Schritte zur Lösung

y^{''} (x) + 16 y = 32 sec (2 x)

Solve linear ODE:

y = c_{1} cos (4 x) + c_{2} sin (4 x) + 8 cos (2 x) cos (4 x) + 4 (- ln (tan (2 x) + sec (2 x)) + 2 sin (2 x)) sin (4 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) + 8 cos (2 x) cos (4 x) + 4 (- ln (tan (2 x) + sec (2 x)) + 2 sin (2 x)) sin (4 x)

(d^{2} - 2 d + 5) y = e^{x}

(d^{2} + 1) \cdot y = x \cdot cos (x)

(d^{2} - 4 d + 4) y = e^{2} x + sin^{2} (x)

(d^{2} - 1) \cdot y = x \cdot sinh (x)

y^{^{''}} + y = 12 x