y^{''}+y= x/(|x|)

Lösung

y^{^{''}} + y = \frac{x}{∣ x ∣}

y = c_{1} cos (x) + c_{2} sin (x) + cos (x) \cdot \int - \frac{x sin ( x )}{∣ x ∣} d x + sin (x) \cdot \int \frac{x cos ( x )}{∣ x ∣} d x

Schritte zur Lösung

y^{''} (x) + y = \frac{x}{∣ x ∣}

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + cos (x) \cdot \int - \frac{x sin ( x )}{∣ x ∣} d x + sin (x) \cdot \int \frac{x cos ( x )}{∣ x ∣} d x

y = c_{1} cos (x) + c_{2} sin (x) + cos (x) \cdot \int - \frac{x sin ( x )}{∣ x ∣} d x + sin (x) \cdot \int \frac{x cos ( x )}{∣ x ∣} d x

(D^{2} + 5 D + 6) y = x^{2} + 2 x

490 y^{^{''}} + 20 y = 8 cos (6 t)

\frac{d ^{2} y}{d x ^{2}} - 4 y = \frac{e ^{2 x}}{x}

2 y^{^{''}} + 3 y^{^{'}} + 3 = cos (x)

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 4 + 6 sin (x)