(d^2+4)y=sin^2(2x)

Lösung

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

y = c_{1} cos (2 x) + c_{2} sin (2 x) + (cos^{4} (x) - \frac{2}{3} cos^{6} (x)) cos (2 x) + \frac{1}{24} (sin (6 x) - 3 sin (2 x) cos (4 x)) sin (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + (cos^{4} (x) - \frac{2}{3} cos^{6} (x)) cos (2 x) + \frac{1}{24} (sin (6 x) - 3 sin (2 x) cos (4 x)) sin (2 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + (cos^{4} (x) - \frac{2}{3} cos^{6} (x)) cos (2 x) + \frac{1}{24} (sin (6 x) - 3 sin (2 x) cos (4 x)) sin (2 x)

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

y^{^{''}} - y^{^{'}} - 6 y = 3 x - 1

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

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

(d^{2} + d - 6) y = e^{2} x \cdot sin^{3} (x)