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Question

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

a) xey+x2=C

b) xey+y2=C

c) yex+x2=C

d) yey+x2=C


Solution

Given, differential equation is exdy+(yex+2x)dx=0
exdydx+yex+2x=0dydx+y=2xex
This is a linear differential equation of the form
dydx+Py=Q
On comparing, P=1 and Q=2xexIF=e1dx=ex
The generalsolution of the given differential equation is given by
y.IF=(2xex×ex)dx+Cyex=2xdx+Cyex=x2+Cyex+x2+C, Hence, the correct option is (c).


Mathematics

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