I am told I can solve the following differential equation by utilising Euler's method. I can solve simple differential equations with the method, I am however, having some trouble wrapping my head around this problem.
$F_thrust$ = Force applied to aircraft
$C_D$ = drag coefficient
$ρ$ = air density
$A$ = wing area
$v^2$ = airspeed in m/s
As mentioned I am a bit stumped by this so any pointers would be great appreciated.
Your diff. equation is briefly written as it follows: $$\frac{dv}{dt} = f(t,v)\tag1$$
If we mesh the time from $t^0$ to $t^N$ making steps of length $\delta t=(t^N-t^0)/N$, one can approximate the derivative of $v$ with respect to time (forward $\textit{Taylor}$'s expansion) as $$\left(\frac{dv}{dt}\right)^{n}\approx \frac{v^{n+1}-v^{n}}{\delta t}$$ Hence the equation $(1)$ can be discretised $$\frac{v^{n+1}-v^{n}}{\delta t}=f(t^n,v^n)$$ Rearranging terms one obtains the explicit method, called $\textit{Euler}$'s method $$v^{n+1} = v^n+\delta t\,f(t^n,v^n)\tag2$$
From wher, provided one initial contition, $\textit{i.e.}$ $v^0=v_0$, recursively from $(2)$ one can obtain the rest of the values of the solution.