(d^2+9)y=cos^2(x)

Lösung

(d^{2} + 9) y = cos^{2} (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{1}{6} cos (3 x) (- \frac{1}{3} cos (3 x) + \frac{1}{2} (- \frac{1}{5} cos (5 x) - cos (x))) + \frac{1}{3} sin (3 x) (\frac{1}{3} cos^{2} (x) sin (3 x) + \frac{1}{6} (sin (x) - \frac{1}{5} sin (5 x)))

Schritte zur Lösung

(d^{2} + 9) y = cos^{2} (x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{1}{6} cos (3 x) (- \frac{1}{3} cos (3 x) + \frac{1}{2} (- \frac{1}{5} cos (5 x) - cos (x))) + \frac{1}{3} sin (3 x) (\frac{1}{3} cos^{2} (x) sin (3 x) + \frac{1}{6} (sin (x) - \frac{1}{5} sin (5 x)))

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{1}{6} cos (3 x) (- \frac{1}{3} cos (3 x) + \frac{1}{2} (- \frac{1}{5} cos (5 x) - cos (x))) + \frac{1}{3} sin (3 x) (\frac{1}{3} cos^{2} (x) sin (3 x) + \frac{1}{6} (sin (x) - \frac{1}{5} sin (5 x)))

(d^{4} - 1) \cdot y = sin (x)

(d^{3} - d^{2} + d - 1) y = 4 sin (x)

(d^{2} - 2 d - 3) y = 5

(d^{3} - d) \cdot y = x

(d^{2} + 2 d + 3) y = sin (x)