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Question

The general solution of the differential equation exdy+(yex+2x)dx=0 is

A
xey+x2=C
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B
xey+y2=C
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C
yexx2=C
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D
yex+x2=C
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Solution

The correct option is D yex+x2=C
exdy+(yex+2x)dx=0
exdy=(yex+2x)dx
dydx+y=2x.ex which is an exact DE
IF=e1dx=ex
General solution is given by

y IF=IF .Q(x) dx+C

yex=ex(2xexdx)+C
yex=x2+C

yex+x2=C

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