Question

Question #91a43

Answer 1

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.

Explanation:

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,..`