Optimizing Thought Processes for Solving Differential Equations

[luckyducky87]

Hello physics forum, can someone please explain to me the thought process that one uses to solve a question like this?



A leak has been discovered in a water supply pipe that will take several days to repair. Suppose that it is leaking at a rate given by the function 4 + 0.2t, that is

dV/dt = 4 + 0:2t

where V is the number of litres of water wasted after t hours. How much water will be wasted as a function of t if after 10 hours there has been 100 litres lost?

Cheers

 

[darkside00]

you have the rate of volume loss of water, dv/dt. The idea is to come up with a function of volume (only) with respect to time t. you have boundary conditions of V(t)=V(10)=100

 

[MisterMan]

My process would be first to identify the kind of differential equation it is, to me it looks like a first order separable differential equation. What I would do is get dV on one side and dt on the other, then I would integrate both sides putting the constant of integration on the t side of the equation since it is V that is a function of t.

Then I would plug in the values it gives you to get the value of the constant. Then you have obtained the particular solution of the differential equation. Let me know how you get on