How to Solve Basic Algebra Questions: Tips and Tricks

[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?)

 

[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!

 

[HallsofIvy]

There is, in fact, no "law" against dividing by several things at the same time: you could go from e^xy'= (4x+ 1)y² to
\frac{y'}{y^2} = \frac{4x+1}{e^x}
by dividing both sides by e^xy²
OR by first dividing by y² and THEN dividing by e^x. The math doesn't care.

 

[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