If `phi(x)` is a differentiable function, then the solution of the different equation `dy+{y phi' (x) - phi (x) phi'(x)} dx=0,` is

The solution of differential equation (dy)/(dx)=y/x+(phi(y/x))/(phi'(y/x)) is

If y=x/(In|cx|) (where c is an arbitrary constant) is the general solution of the differential equation (dy)/(dx)=y/x+phi(x/y) then function phi(x/y) is:

If phi(x) is a differentiable function AAx in Rand a inR^(+) such that phi(0)=phi(2a),phi(a)=phi(3a)and phi(0)nephi(a), then show that there is at least one root of equation phi'(x+a)=phi'(x)"in"(0,2a).

If phi (x) is a differentiable real valued function satisfying phi (x) +2phi le 1 , then it can be adjucted as e^(2x)phi(x)+2e^(2x)phi(x)lee^(2x) or (d)/(dx)(e^(2)phi(x)-(e^(2x))/(2))le or (d)/(dx)e^(2x)(phi(x)-(1)/(2))le0 Here e^(2x) is called integrating factor which helps in creating single differential coefficeint as shown above. Answer the following question: If p(1)=0 and dP(x)/(dx)ltP(x) for all xge1 then

The general solution of the differential equation, y^(prime)+yphi^(prime)(x)-phi(x)phi^(prime)(x)=0 , where phi(x) is a known function, is

If the general solution of the differential equation y'=y/x+phi(x/y) , for some function phi is given by y ln|cx|=x , where c is an arbitray constant, then phi(x/y) is equal to (here y'=(dy)/(dx) )

If the general solution of the differential equation y'=y/x+phi(x/y) , for some function phi is given by y ln|cx|=x , where c is an arbitray constant, then phi(2) is equal to (here y'=(dy)/(dx) )

If phi(x) is a differential real-valued function satisfying phi'(x)+2phi(x)le1, then the value of 2phi(x) is always less than or equal to …….

If phi(x) is a diferential real-valuted function satisfying phi'(x)+2phi(x)le1. prove that phi(x)-(1)/(2) is a non-incerasing function of x.

int e^x {f(x)-f'(x)}dx= phi(x) , then int e^x f(x) dx is