<Dd> f n (x) d n y d x n + ⋯ + f 1 (x) d y d x + f 0 (x) y = g (x) (\ displaystyle f_ (n) (x) (\ frac (\ mathrm (d) ^ (n) y) (\ mathrm (d) x ^ (n))) + \ cdots + f_ (1) (x) (\ frac (\ mathrm (d) y) (\ mathrm (d) x)) + f_ (0) (x) y = g (x)) </Dd> <Dl> <Dd> y (x 0) = y 0, y ′ (x 0) = y 0 ′, y" (x 0) = y 0", ⋯ (\ displaystyle y (x_ (0)) = y_ (0), y' (x_ (0)) = y'_ (0), y' ' (x_ (0)) = y' ' _ (0), \ cdots) </Dd> </Dl> <Dd> y (x 0) = y 0, y ′ (x 0) = y 0 ′, y" (x 0) = y 0", ⋯ (\ displaystyle y (x_ (0)) = y_ (0), y' (x_ (0)) = y'_ (0), y' ' (x_ (0)) = y' ' _ (0), \ cdots) </Dd> <P> For any nonzero f n (x) (\ displaystyle f_ (n) (x)), if (f 0, f 1, ⋯) (\ displaystyle \ (f_ (0), f_ (1), \ cdots \)) and g (\ displaystyle g) are continuous on some interval containing x 0 (\ displaystyle x_ (0)), y (\ displaystyle y) is unique and exists . </P>

Where can simultaneous equations be used in real life