Question

solve:

$(1+x) dy/dx +(x+2)y =2e^{-x}$

Answer 1

"Given (1 + x) dy.dx + (x + 2) y = 2e^-x re - writing eq 1 as dy/dx + p (x) y = Q (x) and comparing, we get dividing ""x + 1"" on both sides of eq 1 we get dy/dx + (x + 2/x - 1) middot y = 2 e^-x/x + 1 compare 3 with 2 we get p(x) = x + 2/x + 1, Q (x) = 2 e^-x/x + 1 Since given equation is linear differential equation of 1^st order in terms of 'y' therefore G middot s = > y middot (I.F) = integral Q (x) middot (I middot F) dx + C where I.F = e^integral p (x) dx I.F = Integrating factor I.F = e^integral x + 2/x + 1 dx e^integral x + 1 + 1/x + 1 dx c^integral x + 1/x + 1 dx + integral 1/x + 1 dx I.F = e^integral 1 dx + integral 1/x "