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Write the integrating factor of the following differential equation: (1+y^2) dx−(tan^−1 (y-x)) dy=0 - Mathematics

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Write the integrating factor of the following differential equation:

(1+y2) dx(tan1 yx) dy=0

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Solution

(1+y2)dx(tan1yx)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)`

Concept: Formation of a Differential Equation Whose General Solution is Given
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