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" (ii) "(x+1)(dy)/(dx)-my=e^(x)(x+1)^(n+...

" (ii) "(x+1)(dy)/(dx)-my=e^(x)(x+1)^(n+1)

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The integrating factor of the differential equation (x+1)(dy)/(dx)-ny=e^(x)(x+1)^(n+1) is -

(x-y)(1-(dy)/(dx))=e^(x)

(dy)/(dx)=(e^(2x)+1)/(e^(x))

Solve : (x+1) dy/dx - ny = e^(x) (x+1) ^(n+1)

Solve (1)/(x)(dy)/(dx)+y.e^(x)=e^((1-x)e^(x))

Find (dy)/(dx) of e^x(1+x)

The solution of (1)/(x)(dy)/(dx) + y e^(x) = e^((1-x)^(e^(x))) is

(1+x^(2))(dy)/(dx)+y=e^(tan^(-1)x)

(1+x^(2))(dy)/(dx)+y=e^(tan^(-1)x)

(1+x^(2))(dy)/(dx)+y=e^(tan^(-1)x)