An integrating factor for the linear differential equation $y ^ { \prime } + y / x = x$ is
A) $1 / x$
B) $x$
C) $1 / x ^ { 2 }$
D) $x ^ { 2 }$
E) $e ^ { - x }$

Question

Quizplus · Accepted Answer

The integrating factor for a linear differential equation of the form $y' + P(x)y = Q(x)$ is $e^{\int P(x) dx}$. Here, $P(x) = 1/x$, so the integrating factor is $e^{\int 1/x dx} = e^{\ln|x|} = x$ for $x > 0$.

An Integrating Factor for the Linear Differential Equation y′+y/x=xy ^ { \prime } + y / x = xy′+y/x=x

An Integrating Factor for the Linear Differential Equation $y ^ { \prime } + y / x = x$