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

Question

Quizplus · Accepted Answer

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

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 $y ^ { \prime } - y / x = x$