Consider the following ODE with given IC: Y^{\prime}(x)=x^{2} \cos (Y(x))^{2}, Y(0)=1 \text { and answer the following questions: } \text { What is } \frac{\partial f(x, z)}{\partial z} ? In what region of x will the solution exist? c) Find the analytical solution Y(x) and verify where it exists.

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6