We have;
dxdy+ycot(x)=1⇒dxdy+ysin(x)cos(x)=1
The Integrating Factor (I.F) of the DE is;
e∫sin(x)cos(x) dx=eln∣sin(x)∣=sin(x)
Multiplying the I.F by the given DE yields;
(dxdy+ysin(x)cos(x))sin(x)=1×sin(x)⇒dxd(ysin(x))=sin(x)⇒ysin(x)=∫sin(x) dx⇒ysin(x)=−cos(x)+a, where a is an arbitrary constant.⇒y=sin(x)a−cos(x)
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