If `x(dy)/(dx)=x^(2)+y-2, y(1)=1`, then `y(2)` equals ………………..

If y=y(x) and (2+sinx)/(y+1)((dy)/(dx))=-cosx ,y(0)=1, then y(pi/2) equals

If y = y(x) is the solution of the differential equation, x dy/dx+2y=x^2 satisfying y(1) = 1, then y(1/2) is equal to

If y= y(x) ( 2 _ cos x ) /( y+1) (( dy )/(dx)) =- sin x, y (0) =1 then y((pi)/(2)) equal ____.

If y(x) is the solution of the differential equation (dy)/(dx)=-2x(y-1) with y(0)=1 , then lim_(xrarroo)y(x) equals

If y(x) is the solution of the differential equation (dy)/(dx)=-2x(y-1) with y(0)=1 , then lim_(xrarroo)y(x) equals

(dy)/(dx)=(x+y+1)/(2x+2y+3)

If y=x^(x^(2)), then (dy)/(dx) equals

If y=f(x) satisfies the differential equation (dy)/(dx)+(2x)/(1+x^(2))y=(3x^(2))/(1+x^(2)) where f(1)=1 , then f(2) is equal to

If y=y(x) and ((2+sinx)/(y+1))dy/dx=-cosx, y(0)=1 , then y(pi/2) equals (A) 1/3 (B) 2/3 (C) -1/3 (D) 1

If (dy)/dx = (xy)/(x^2 + y^2), y(1) = 1 and y(x) = e then x =