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(dy)/(dx) =-(y+sinx)/(x) satisfying cond...

`(dy)/(dx) =-(y+sinx)/(x)` satisfying condition `y(0)=1`

Text Solution

Verified by Experts

The correct Answer is:
`cosx=xy+1`
We have `-xdy=ydx+sinxdx`
`therefore -sinx dx=x dy+ydx`
`rArr -sinx dx=d(xy)`
`rArr int(-sinx)=intd(xy)`
`rArr cosx=xy+c`
Given that `y(0)=1`
`therefore c=1`
So, required particular solution is `cosx=xy+1`
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