# Differential equation problem

1. Apr 27, 2015

### Raghav Gupta

1. The problem statement, all variables and given/known data
A particle moves in a straight line with velocity given by $dx/dt = x +1$ ( x being distance described). The time taken by the particle to describe 99 meters is?

2. Relevant equations
NA

3. The attempt at a solution
Getting $ln(x+1) = t + C$
How to determine the constant value when we don't know any (x,t) point?

2. Apr 27, 2015

### MarcusAgrippa

This particular problem cannot be fully solved without initial conditions. These are used to evaluate C. Did you miss them when reading the problem?

If the question truly omits the initial conditions, there is nothing to stop you from solving the problem symbolically by retaining the constant of integration C in your solution. and express the answer in terms of C.

If you feel unhappy with retaining C as an unknown parameter, you could always assume some initial conditions - but make sure that you state explicitly what conditions you have assumed; state also why you were forced to make the assumption. No one can penalise you for displaying that you understand the problem and its deficiencies.

The obvious assumption to import is that at t=0, x=0.

Your working is correct so far.

Remember that your tutors and examiners are not interested in the answer - they know the answer and have no need to be told it by you! Rather, they are interested in seeing how you reasoned your way to the answer. If you display good reasoning, you will be awarded full marks if the statement of the question was at fault, and you will be awarded close to full marks if you missed information by careless reading but nevertheless give an accurate answer in which the missing information is displayed symbolically.

3. Apr 27, 2015

### Raghav Gupta

No, I was not given any additional info.
By the way this was an Objective question and not subjective, so they not require the reason.
That info of taking x=0 at t= 0 looks correct to me as at time 0 particle is at rest.
Thanks, got it Marcus.

4. Apr 27, 2015

### LCKurtz

You probably mean the particle is at position $x=0$.

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