110. Find the general solution of the equation $y^{\prime \prime}=4 x$.
Solution. We have

$$
\begin{gathered}
\frac{d y^{\prime}}{d x}=4 x ; d y^{\prime}=4 x d x ; y^{\prime}=4 \int x d x=2 x^{2}+C_{1} \\
\frac{d y}{d x}=2 x^{2}+C_{1} ; d y=\left(2 x^{2}+C_{1}\right) d x \\
y=\int\left(2 x^{2}+C_{1}\right) d x=2 \int x^{2} d x+C_{1} \int d x=\frac{2}{3} x^{3}+C_{1} x+C_{2}
\end{gathered}
$$

Let's verify the obtained result by differentiation:

$$
y^{\prime}=\frac{2}{3} \cdot 3 x^{2}+C_{1}=2 x^{2}+C_{1} ; y^{\prime \prime}=4 x
$$