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

The solution to the differential equation ylogy+x y^(prime)=0, where y(1)=e , is

The general solution of the differential equation (dy)/(dx)+y\ g^(prime)(x)=g(x)g^(prime)(x) , where g(x) is a given function of x , is a. g(x)+log{1+y+g(x)}=C b. g(x)+log{1+y-g(x)}=C c. g(x)-log{1+y-g(x)}=C d. None of these

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

The solution of differential equation y y^(prime)=x((y^2)/(x^2)+(f((y^2)/(x^2)))/(f^(prime)((y^2)/(x^2)))) 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:

Solve (dy)/(dx)+y phi'(x)=phi(x).phi'(x), "where" " "phi(x) is a given function.

Solve (dy)/(dx)=(yphi'(x)-y^(2))/(phi(x)),"where" " "phi(x) is a given function.

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