\(\[\begin{align} & Temos: \\ & \frac{{{y}'}}{y}=2x \\ & \int{\frac{dy}{y}}=\int{2}xdx\int{\frac{dy}{y}} \\ & 2\int{x}dx\operatorname{l} \\ & \log o: \\ & ln(y)=2\cdot \frac{{{x}^{2}}}{2}+C \\ & \ln (y)={{x}^{2}}+C~~(i) \\ & \ln (y)={{x}^{2}}+C\ln (e) \\ & {{3}^{2}}+C1=9+CC=-8 \\ & substituindo: \\ & \ln (y)={{x}^{2}}+C \\ & \ln (y)={{x}^{2}}-8 \\ & y(x)={{e}^{{{x}^{2}}-8}} \\ & y(2)={{e}^{{{2}^{2}}-8}} \\ & y(2)={{e}^{4-8}} \\ & y(2)={{e}^{-4}} \\ \end{align}\] \)