31. Find the particular solution of the differential equation $d y=\left(x^{2}-1\right) d x$, if $y=4$ when $x=1$.
Solution. We have $\int d y=\int\left(x^{2}-1\right) d x ; y=\frac{x^{3}}{3}-x+C ; \quad 4=\frac{1}{3}-$ $-1+C$, from which $C=\frac{14}{3}$. Therefore, we obtain the answer: $y=\frac{x^{3}}{3}-x+\frac{14}{3}$.