First slide
Introduction to Differential equations
Question

 Let f:[0,1]R be such that f(xy)=f(x)f(y)x,y[0,1] and f(0)0 . If y=y(x)  satisfies the differential equation dydx=f(x) with y_(0)=1 then y(1/4)+y(3/4) is 

Easy
Solution

 f(x)=1dydx=f(x)=1 given dy=dxy=x+1y(0)=1c=1y=x+1y(1/4)+y(3/4)=14+34+2=3

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