LINEAR TYPE DIFFERENTIAL EQUATION (Excercise Problems)

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

\[1.\ \color{red}{Find\ the\ integrating\ factor\ of\ \frac{dy}{dx}\ +\ \frac{2}{x}\ y\ =\ x}\ \hspace{15cm}\]

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

\[2.\ \color{red}{Find\ the\ integrating\ factor\ of\ \frac{dy}{dx}\ +\ y\ tan\ x\ =\ x^2}\ \hspace{15cm}\]

\[3.\ \color{red}{Find\ the\ integrating\ factor\ of\ \frac{dy}{dx}\ -\ y\ cot\ x\ =\ sin\ x}\ \hspace{15cm}\]

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

\[4.\ \color{red}{Solve:\ \frac{dy}{dx}\ -\ \frac{2}{x}\ y\ =\ x^2\ sin\ x}\ \hspace{15cm}\]

\[5.\ \color{red}{Solve:\ \frac{dy}{dx}\ +\ y\ tan\ x\ =\ e^x\ cos\ x}\ \hspace{15cm}\]

\[6.\ \color{red}{Solve:\ \frac{dy}{dx}\ -\ y\ tan\ x\ =\ e^x\ sec\ x}\ \hspace{15cm}\]

\[7.\ \color{red}{Solve:\ \frac{dy}{dx}\ +\ y\ tan\ x\ =\ cos^3\ x}\ \hspace{15cm}\]

\[8.\ \color{red}{Solve:\ \frac{dy}{dx}\ +\ y\ cot\ x\ =\ 2\ cos\ x}\ \hspace{15cm}\]