If `dy/dx+[2y]/x=0`, y(1)=1,then y(2)=

If (dy)/(dx)= y sin 2x, y(0)=1 , then solution is

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

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

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

If (1+x^(2))(dy)/(dx)=1+y^(2),y(0)=1, then y(2)=

If x dy =y (dx+y dy), y(1) =1 and y(x)gt 0 . Then, y (-3) is epual to

For each of the following initial value problems verify that the accompanying functions is a solution. (i) x(dy)/(dx)=1, y(1)=0 => y=logx (ii) (dy)/(dx)=y , y(0)=1 => y=e^x (iii) (d^2y)/(dx^2)+y=0, y(0)=0, y^(prime)(0)=1 => y=sinx (iv) (d^2y)/(dx^2)-(dy)/(dx)=0, y(0)=2, y^(prime)(0)=1 => y=e^x+1 (v) (dy)/(dx)+y=2, y(0)=3 => y=e^(-x)+2

If x dy =y (dx+y dy), y(1) =1 and Y(x)gt 0 . Then, y (-3) is epual to

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