Question #91a43

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Answer 1 · 2016-06-05T09:17:05

A rounded 5-sd set of solutions is
$x = (4n +0.76528) pi, n=0, +-1, +-2, +-3, ...$ .
Of course, $x =0, +-2pi, +-4pi, +-6pi, ..$ are also solutions.

Let $y(x)=sin x + 1.5 sin (1.5 x )$

This represents the compounded oscillation of the separate

oscillations for sin x and 1.5 sin (1.5 x ) of periods $2pi and (4pi)/3$ ,

respectively.

Now, $y(x+4pi)=y(x)$ . So, y is periodic with period $4pi$ .

I have obtained one approximate solution from

$y(137,753^o) = y(0.76528 pi)=0.000001$ , nearly.

This 5-sd solution $in (0, 2pi)$ was obtained by using a

convergent root-bracketing (optimized bisection) method.

Correspondingly, the set of genera(.solutions is obtained as

$x = (4n +0.76528) pi, n=0, +-1, +-2, +-3, ...$

Likewise, another such root $in (2pi, 4pi)$ could be approximated.

Correspondingly, one more set of general solutions

could be obtained.

Indeed, y becomes 0, for x= $2npi, n=0,+-1,+-2,+-3,..$