9.1 (nat) let f: r+r be a differentiable function such that f'(a) = fr) for all ze . suppose that f[ar) ancd f(57) are two nonzero solution ot the tollowing dif

9.1 (NAT) Let f: R+R be a differentiable function such that f'(a) = fr) for all zE . Suppose that f[ar) ancd f(57) are two nonzero solution ot the tollowing differential equation ,dy rPd + 3y =0 satistying f(ar)f(3r)= f(2r) and f(or)f(-Br) = f(r) then value of p is given by Q.2 (NAT) equation lf g(r) = Ae" +e #2 be the solution of the following differential dy -6y=0 da? dr satistying 0)=5 then y(0) equals Q.3 (MCQ) Let z, I+e", 1 +r+e" be the solution of a second order linear differ- ential equation with constant coetticients. If y(r) is the solution of same differential equation satistying g(0)=3 and 0) =4 the y(1) equals (a) e+l (b) 2e+3 (c) 3e+2 (d) 3e+2 Q.4 (NAT) If y(r) is the solution of following differential equation d++4y-0 v0)-2 -0 then y(log2) equals. Q.5 (NAT) If g(r) be the solution of the following differential equation satishes y(0)=I and 0)-I then y(T) attains its maximum at

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