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

解

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

解答ステップ

y^{''} (x) + y = \frac{x}{∣ x ∣}

線形 ODE を解く:

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