Function the functionality of the function

Calculus Level 5

$\large \int y(2x) \ dy=2 \int \left(y(2x)-y\right) \ dx$

In the equation above, $y$ is a function of $x$ and $y \ne x$ . Find the value of $y$ when $x=2$ . Give your answer correct to 3 significant figures.

1 solution

Andrew Ho
Nov 1, 2017

Let's rearrange this.

$y(2x)y'$ = $2[y(2x)-y(x)]$ . So, $2y(x)-y'y(2x)=2y$ , $y(2x)(2-y')=2y$ . Therefore we arrive with $y(2x)=$ $\frac{2y}{2-y'}$ .

Now, using previous knowledge we have from the trigonometric double angle formulas, $y=tanx$ .

So the answer is tan(2), which is -2.19 to 3 significant figures.