Let (x) be an integrating factor for y ' P(x)y Q(x) The differential equation y ' P(x)y 0 is called the associated homogeneous equation (a) Show that y 1 (x) is a solution of the associated homogeneous equation (b) Show that if y (x) is a particular solution of y ' P(x)y Q(x), then (x) C (x) is also a solution for any constant C

Question: Let (x) be an integrating factor for y' + P(x)y = Q(x). The differential equation y' + P(x)y = 0 is called the associated homogeneous

Let α(x) be an integrating factor for y' + P(x)y = Q(x). The differential equation y' + P(x)y = 0 is called the associated homogeneous equation.
(a) Show that y = 1/α(x) is a solution of the associated homogeneous equation.
(b) Show that if y = ƒ(x) is a particular solution of y' + P(x)y = Q(x), then ƒ(x) + C/α(x) is also a solution for any constant C.

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