### It's Only a Minus Sign

Solve these differential equations to see how a minus sign can change the answer

### Differential Equation Matcher

Match the descriptions of physical processes to these differential equations.

### Taking Trigonometry Series-ly

Look at the advanced way of viewing sin and cos through their power series.

# Weekly Challenge 42: What's My Equation?

##### Stage: 5 Challenge Level:

The solution is:

$$X(t) = K \exp\left(\log\left(\frac{X(0)}{K}\right)\exp(-\alpha t)\right)$$

Can you find a nice differential equation which this solutionÂ satisfies?

The solution is:

$$P(t) = \frac{a\exp(bt)}{a-1+exp(bt)}$$

Can you find a nice differential equation which this solutionÂ satisfies?

Did you know ... ?

There is a branch of mathematics concerned with solving so-called 'inverse-problems'. In an inverse problem you begin with a solution, or some partial solution, and attempt to construct the equations or theories which might give rise to it. The first solution in this problem is called the Gomperz function and is used to model the size of tumors. Perhaps you might discover the uses for the second solution?