Question

Partial differential equation

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} ?

c) Find the analytical solution Y(x) and verify where it exists.

In what region of x will the solution exist?


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