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Solve e^((dy)/(dx))=x+1, given that when...

Solve `e^((dy)/(dx))=x+1,` given that when `x=0,y=3.`

Text Solution

Verified by Experts

The correct Answer is:
`y=(x+1)(log_(e)(x+1))-x+3`
`e^((dy)/(dx))=x+1`
or `(dy)(dx) = log(x+1)`
or `intdy=intlog(x+1)dx`
or `y=(x+1)log(x+1)-x+c`
when x=0, y=3 is c=3
Hence, the solution is `y=(x+1)log(x+1)-x+3`
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