The integrating factor of the linear directional equation d y d x +P(x) y=Q(x) is a solution of the differential equation

Step-by-step solution

d y d x +P(x) y=Q(x) aligned & Integrating =e^ P(x) d x & Factor aligned (A) If y=e^ p(x) d x checking: d y d x -P(x) y=0 d y d x =e^ p (x) d x P(x)=y P(x) P(x) y-y P(x)=0 Hence found If of d y d x +P(x) y=Q(x) i.e., e^ p(x) d x is the solution of (A) ie;, d y d x -P(x) y=0