# Basic Algebra Questions

1. Mar 27, 2006

### kape

I have a few nagging questions that are preventing me from solving calculus problems.. Can someone give me a hand?

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Question 1

$$e^xy' = (4x+1)y^2$$

From the equation above, is it possible to do this:

$$\frac{y'}{y^2} = \frac{4x+1}{e^x}$$

Aren't you supposed to divide one at a time, like this?

$$\frac{e^xy'}{y^2} = (4x+1)$$

How would I get the $$\inline e^x$$ to the other side?

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Question 2

How do you tell the difference between these two?

$$2 - 3 = -1$$ and $$2-3 = -6$$ ?

(One latter being (2)(-3) = - 6?)

2. Mar 27, 2006

### assyrian_77

Q1. Yes, it is possible. How to get the $e^x$ to the other side? Just divide both sides by $e^x$. Which is the same as your first statement.

Q2. What do you mean? One DOES NOT write $2\cdot(-3)$ as $2-3$!

3. Mar 28, 2006

### HallsofIvy

Staff Emeritus
There is, in fact, no "law" against dividing by several things at the same time: you could go from exy'= (4x+ 1)y2 to
$$\frac{y'}{y^2} = \frac{4x+1}{e^x}$$
by dividing both sides by exy2
OR by first dividing by y2 and THEN dividing by ex. The math doesn't care.

4. Mar 29, 2006

### J77

I guess the dash represents differentiating w.r.t x...

$$e^x \frac{dy}{dx}=(4x+1)y^2$$

$$\frac{1}{y^2}\frac{dy}{dx}=\frac{(4x+1)}{e^x}$$

$$\int_y{y^{-2}}dy=\int_x{(4x+1)e^{-x}dx$$