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

Write the integrating factor of the following differential equation:

(1+y2) dx(tan1 yx) dy=0

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)

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