Y=(x1)(x2)/x^1/2 = (x^23x2)/x^1/2 dy/dx=√x(2x3)1/2√x(x^23x2)/(√x)^2 dy/dx =2x(2x3)(x^23x2)/2x√xx dy/dx =4x^2–6xx^23x2/2x√x dy/dxQ If y = 2^x, find dy/dx ANSWER 1) Take Logs of both sides of our equation y = 2^x So we get log (y)=log (2^x) 2) Apply relevant log rule to rhs Log rule log (a^b) = b log (a) nb the dot between b and log (a) represents x / multiply / times ) So we get log (y) = x log (2) Transcript Ex 96, 3 For each of the differential equation given in Exercises 1 to 12, find the general solution = 2 = 2 Differential equation is of the form = where P = 1 and Q = x2 Finding integrating factor, IF = e IF = e 1 IF = e log IF = x Solution is y (IF) = yx = 2
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