## Related questions with answers

Question

In this exercise, let $\alpha(x)$ be an integrating factor for $y^{\prime}+P(x) y=Q(x)$. The differential equation $y^{\prime}+P(x) y=0$ is called the associated homogeneous equation.

(a) Show that $y=1 / \alpha(x)$ is a solution of the associated homogeneous equation.

(b) Show that if $y=f(x)$ is a particular solution of $y^{\prime}+P(x) y=Q(x)$, then $f(x)+C / \alpha(x)$ is also a solution for any constant $C$.

Solution

VerifiedStep 1

1 of 4We are given the equation:

$y'+P(x)y=Q(x)$

and its associated homogeneous equation:

$y'+P(x)y=0$

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