Make an appropriate substitution to find a solution of the equation dy/dx=sin(x-y). Does this general solution contain the linear solution y(x)=x-pi/2 that is readily verified by substitution in the differential equation?(adsbygoogle = window.adsbygoogle || []).push({});

Here's what I did:

v=x-y

y=x-v

y'=1-dv/dx

1-dv/dx=sin(v)

1-sin(v)=dv/dx

dx=dv/(1-sin(v))

x=2/(cot(v/2)-1)

The solution in the back of the book gives:

x=tan(x-y) + sec(x-y)

What am I doing wrong?

Any help is greatly appreciated.

Thanks!

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# Homework Help: Substitution in Differential Equations

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