`(dy)/(dx)+(y)/(x)=(y^(2))/(x)log x`

The solution of (dy)/(dx)+(y)/(x)=(1)/((1+log x+log y)^(2)) is given by

Solve (dy)/(dx)+(y)/(x)=log x.

If x^(y) y^(x)=5 , then show that (dy)/(dx)= -(log y + (y)/(x))/(log x + (x)/(y))

The solution of the differential equation x(dy)/(dx)=y ln ((y^(2))/(x^(2))) is (where, c is an arbitrary constant)

If (x)/(x-y)=log((a)/(x-y)) then (dy)/(dx) is (a) (x)/(y), (b) 2-(x)/(y), (c) 2, (d) (x-y)/(x)

If x=y log(xy) , then prove that (dy)/(dx) = (y (x-y))/(x(x+y)) .

If x y\ log(x+y)=1 , prove that (dy)/(dx)=-(y(x^2y+x+y))/(x(x y^2+x+y)) .

The solution of (dy)/(dx)=(x+y-1)+(x+y)/(log(x+y)), is given by

If y=xlog(x/(a+b x)),t h e nx^3(d^2y)/(dx^2)= (a) x(dy)/(dx)-y (b) (x(dy)/(dx)-y)^2 y(dy)/(dx)-x (d) (y(dy)/(dx)-x)^2

Which of the following differential equations has y = x as one of its particular solution? (A) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=x (B) (d^2y)/(dx^2)+x(dy)/(dx)+x y=x (C) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=0 (D) (d^2y)/(dx^2)+x(dy)/(dx)+x y=0