form a differential equation of, y=asinbx
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To form a DE from y=asin(bx), we need to remove at least one of the constants a or b, so let’s differentiate: y'=abcos(bx) and again: y''=-ab²sin(bx).

So y''=-b²y, by substituting y for asin(bx). The DE is y''+b²y=0.

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