having so much trouble with de's in general! i think it's a linear de, but really stuck! please help:
dp/dt = -50 + 15p - p^2
thanks in advance!
There is a in the expression so the equation is not linear. However, the two variables and can be separated : and we'll get the solution by integrating the both sides.
To achieve this, one needs to make appear a derivative on the LHS. As the denominator contains a , one can try to transform into which anti-derivative is . Hence solving this problem boils down to finding . Do you have any idea on how this can be done ?
well i have no idea, but i thought maybe i could try 'flipping' it as the rhs is in terms of p
ie. dt/dp = - 1/(p^2 - 15p + 50)
and then t = - integral[1/(p^2 - 15p + 50)] dp
does that work? i'm not sure if that is how to start the question