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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

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

y^{^{''}} - y^{^{'}} - 6 y = 11

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

(d^{4} - 1) y = e^{x} cos (x) cos^{3} (x)

(d^{2} - 4 d + 4) \cdot y = 8 e^{2 x} \cdot x^{2} \cdot sin^{2} (x)