Question: Consider the variable coefficient ODEx2y''+7xy'+8y=0,x>0You are given that one solution isy1=x-4. Let the other solution bey2(x)=y1(x)u(x).(a) Use reduction of order to obtain an ODE for

Consider the variable coefficient ODEx2y''+7xy'+8y=0,x>0You are given that one solution isy1=x-4. Let the other solution bey2(x)=y1(x)u(x).(a) Use reduction of order to obtain an ODE for w(x)=u'(x). The ODE for w(x)isdw(d)x+(blank)w=0.(b) A solution to the ODE in(a)isw(x)=(c) A second linearly independent solution isy2(x)=You must simplify your answer as much as possible.

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