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The solution of x(dy)/(dx)+y=e^(x)"is"...

The solution of `x(dy)/(dx)+y=e^(x)"is"`

A

`y=(e^(x))/(x)+(k)/(x)`

B

`y=(e^(x))/(x)+(k)/(x)`

C

`y=xe^(x)+k`

D

`x=(e^(y))/(y)+(k)/(y)`

Text Solution

Verified by Experts

Given, that `x(dy)/(dx)+y=e^(x)`
`Rightarrow (dy)/(dx)+(y)/(x)=(e^(x))/(x)`
Which is linear differential equation.
`IF=e^(int(1)/(2)dx)=e^(logx)=x`
The general solution is `y=int((dx)/(x).x)dx`
`Rightarrow y.x.=inte^(x)dx`
`Rightarrow y.x=e^(x)+k`
`Rightarrow y=(e^(x))/(x)+(k)/(x)
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