Chapter 7: Transcendental Functions - Section 7.4 - Exponential Change and Separable Differential Equations - Exercises 7.4 - Page 400: 13

$ 2 \tan \sqrt y=x+c$

Rewrite the given equation and then integrate. We have $\int dx= \int \dfrac{2}{2 \sqrt y \cos^2 \sqrt y} dy$ Plug $a=\sqrt y \implies \dfrac{dy}{2 \sqrt y}=da$ $ \int \dfrac{2}{ \cos^2 a} da=x+c \implies 2 \tan (a)=x+c$ Hence, $ 2 \tan (\sqrt y)=x+c$