Example 1. Solve the equation $y^{IV}=\cos x$.
Solution. The equation belongs to type 1). Integrating:

$$
y^{\prime \prime \prime}=\int \cos x d x, \text { i.e. } y^{\prime \prime \prime}=\sin x+C_{1}
$$

Integrate again: $y^{\prime \prime}=-\cos x+C_{1} x+C_{2}$. Next, by analogy:

$$
y^{\prime}=-\sin x+C_{1} \frac{x^{2}}{2}+C_{2} x+C_{3}
$$

The last integration leads to the answer (find it yourself).

Answer. $y=\cos x+C_{1} \frac{x^{3}}{6}+C_{2} \frac{x^{2}}{2}+C_{3} x+C_{4}$.

Note. The products (quotients from division) of constants by numbers are also constants, so the previous answer can be written in a more convenient form: $y=\cos x+C_{1} x^{3}+C_{2} x^{2}+C_{3} x+$ $+C_{4}$.