Question $1$: $10$ Marks

$(1\mathrm{.}1)By$ using $an$ analytical approach $(do$ not use inspection $as$ marks will $be$ deducted$),$ determine

all the equilibrium point$(s)of$ the following differential equation:

$\frac{dx}{dt}=5(\sqrt[\phantom{2}]{x^2-1}{)}^{-1}-2(\sqrt[\phantom{2}]{x^2-1})-3$

Question $2$: $30$ Marks

Draw the phase lines $of$ the following differential equations. List all the equilibrium points for each system,

and classify them $as$ stable $or$ unstable:

$(2\mathrm{.}1)$

$\frac{dx}{dt}=e^{2ln(x)}+5e^{lnx}-36$

$(2\mathrm{.}2)$

$\frac{dx}{dt}=1-sin(x)$

$(2\mathrm{.}3)$

$\frac{dx}{dt}=e^{ln(x^{logx})}-\frac{x^3}{{10}^4}$