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Question
Write the integrating factor of the following differential equation:
(1+y2) dx−(tan−1 y−x) dy=0
Solution
(1+y2)dx−(tan−1y−x)dy=0
`=>(1+y^2)dx/dy=tan^−1 y−x`
`⇒(1+y^2)dx/dy+x=tan^−1 y`
`⇒dx/dy+1/(1+y^2)x=tan−1y/(1+y^2)`
∴ Integrating factor (IF)= `e^(int 1/(1+y^2)dy)`
`=e^(tav^-1y)`
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