MHB How Do You Rearrange dS/dt = (n-x-rS)(L-1) to Solve for t?

  • Thread starter Thread starter BSLAHi
  • Start date Start date
  • Tags Tags
    Calculus
Click For Summary
To rearrange the equation dS/dt = (n-x-rS)(L-1) to solve for t, separate the variables and integrate. The integration involves the left side being ∫(dS/(n-x-rS)) and the right side as ∫(L-1) dt. This process allows for the determination of t in terms of S and other variables. The integration will yield an expression that can be manipulated to isolate t. This method provides a systematic approach to solving the differential equation.
BSLAHi
Messages
1
Reaction score
0
Hello,

I have been given a general equation that is dS/dt = (n-x-rS)(L-1)
and it needs to be rearranged in order to for the subject to be t.

I have spent a while trying to find a way to attempt this but with no luck
so I will leave this here.

Thanking You,
BSLAHi
 
Physics news on Phys.org
Hello BSLAHi.

You can separate the variables and integrate.
$$\frac{\mathrm dS}{\mathrm dt}\ =\ (n-x-rS)(L-1)$$
$\displaystyle\implies\ \int\frac{\mathrm dS}{n-x-rS}\ =\ \int(L-1)\,\mathrm dt$.
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
View full post »

Similar threads

Graduate The Lagrangian of a free particle ##L=-m \, ds/dt##
  • · Replies 3 ·
Replies
3
Views
811
MHB Are $\vec{r}$ and $\frac{d^2\vec{r}}{dt^2}$ Parallel When m+n=1?
  • · Replies 6 ·
Replies
6
Views
1K
High School Why do I not understand what seems to be basic Calculus?
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Integrating x^ne^xn: Analyzing & Solving
  • · Replies 5 ·
Replies
5
Views
3K
MHB Solving a Difficult Integral: Evaluating \int_{C}^{} \,d \frac{x^3}{y} ds
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How is the derivative of y(x,t) derived in quantum mechanics?
  • · Replies 1 ·
Replies
1
Views
1K
MHB What Is the Total Distance Traveled by the Particle from t = 0 to t = 3?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Why Do Fourier Series Integrations Often Use Different Variables of Integration?
  • · Replies 3 ·
Replies
3
Views
2K
How do I know "what Fourier transform" to use?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Einstein brother-in-law elevator
  • · Replies 11 ·
Replies
11
Views
2K