# Search results

1. ### Tricky Looking!

Think with my poor Tex you missed the x after the 5 on the RHS. Take that into account and you're there.
2. ### Tricky Looking!

If it's just finding the derivative then this is probably more a question for the calculus thread. Anyhoo, i'll do the first part. Take logs to get. ln(y)= 5x ln(4-x) Now differentiate (implicitly on the LHS) and rearrange to get your answer for dy/dx. Have a go and let me know...
3. ### Tricky Looking!

I guess that depends what the question is. Are you asking for the differential equation to which this is the solution? Take logs and differentiate for first order ODE?
4. ### Bacteria Growth Problem.

Yeah that amused me too :smile: .I'd probably start a little earlier: Growth proportional to size implies..... \frac{dy}{dt}=ky with the intial condition y(0)=500 and the time t = 3 (in hours!) condition y(3)=8000. Your mission, should you choose to accept it, is to find the general...
5. ### Help me with Linear equation pls ~

and (b) gives: (.....i'll spare the details but it's the usual integrating factor prob...) y = x(cx - 3) where c is your integration constant. To satisfy the IC y(0) = 0, c can take on any value you want.
6. ### Problem with an ODE

Just to put this problem in a general context, it's form is: \frac {dy} {dx} = a(x) y + b(x) y^p Which is a Bernoulli ODE (or a Ricatti with no constant term). The substitution: u(x) = y^{1-p} reduces this to a first order linear ODE which can be solved in the usual way via an...