FIRST ORDER DIFFERENTIAL EQUATION (Excercise Problems)

\[\underline{PART\ -\ A}\]

\[1.\ \color{red}{Solve:\ sec\ x\ tan\ x\ dx\ +\ sec\ y\ tan\ y\ dy\ =\ 0}\ \hspace{15cm}\]

\[\underline{PART\ -\ B}\]

\[2.\ \color{red}{Solve:\ x\ \frac{dy}{dx}\ =\ y}\ \hspace{18cm}\]

\[3.\ \color{red}{Solve:\ xdx\ -\ ydy\ =\ 0}\ \hspace{18cm}\]

\[4.\ \color{red}{Solve:\ \frac{dy}{dx}\ =\ \frac{1}{1\ +\ x^2}}\ \hspace{18cm}\]

\[\underline{PART\ -\ C}\]

\[5.\ \color{red}{Solve:\ (1\ +y^2)\ dx\ +\ (1\ +\ x^2)\ dy\ =\ 0}\ \hspace{15cm}\]

\[6.\ \color{red}{Solve:\ \frac{dy}{dx}\ =\ \sqrt{\frac{1\ -\ y^2}{1\ -\ x^2}}}\ \hspace{18cm}\]

\[7.\ \color{red}{Solve:\ tan\ x\ sec^2\ y\ dy\ +\ tan\ y\ sec^2\ x\ dx\ =\ 0}\ \hspace{15cm}\]