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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} - y = \frac{2}{( 1 + e ^{x} )}

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

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

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

y^{^{'''}} - 4 y^{^{'}} = 0