Please tell me if I'm on the right track for solving the following system:
$$\frac{d{U}}{dt}=a - b U -\frac{\beta U V}{U+V} \\ \frac{d{V}}{dt}=\frac{\beta U V}{U+V}-(b+c+d)V $$
Steps:
$1.$ I added the two equations to get $$\frac{d{U}}{dt}+b U=a-(b+c+d)V-\frac{d{V}}{dt}$$
$2.$ Then I solved for $U$.
$3.$ Then I solved the equation in Step $1$ for $V$.
$4.$ Now I am plugging in the expression for $U$ into the equation for $V$ (because it looks easier than plugging in the other way around).
Thanks for any help!