سلسلة المعادلة التفاضلية : The differential equations series

\[Solve \: the \, differential\: equations:\, \, Q1a. \, \, \, \frac{\mathrm{d} y}{\mathrm{d} x}=\frac{x}{x^{2}+1}\]


\[Solve \: the \, differential\: equations:\, \,\\ Q1b. \, \, \,\left ( e^{x}+e^{-x} \right )\frac{dy}{dx} =\left ( e^{x}-e^{-x} \right )\]

\[{\color{Blue} Q1-b)}\\(e^{x}+e^{-x})\frac{dy}{dx}=(e^{x}-e^{-x})\\dy=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}dx\\y=ln(e^{x}+e^{-x})+lnC\\y=lnC(e^{x}+e^{-x})\]