Question: [Maximum mark: 8](a) Show that y=(1)/(2x^(2))int f(x)dx is a solution of the differential equation 2x^(2)((d)y)/((d)x)+4xy=f(x)(b) Hence solve 2x^(2)((d)y)/((d)x)+4xy=(1)/(x),x>0, given that y=2 when x=1.
[Maximum mark: 8](a) Show that y=(1)/(2x^(2))\int f(x)dx is a solution of the differential equation 2x^(2)((d)y)/((d)x)+4xy=f(x)(b) Hence solve 2x^(2)((d)y)/((d)x)+4xy=(1)/(x),x>0, given that y=2 when x=1.
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