`(dy)/(dx)=(x+sin x)/(y+cos y)`

Find the particular solution of the differential equation. (dy)/(dx) = ((x sin((x)/(y))-y cos ((x)/(y)))y)/((y cos ((x)/(y))+x sin ((x)/(y)))x) , given that y = 1 when x = (pi)/(4)

Solve the following differential equations. (dy)/(dx )= sin ( x+y) + cos ( x + y)

Find (dy)/(dx) " if " sin x + cos y = xy "

Solution of differential equation (dy)/(dx)=sin(x+y)+cos(x+y) is

Solve (dy)/(dx) + x sin 2y = x^(3) cos^(2) y

The differential equation (dy)/(dx)+x sin 2y=x^(3)cos^(2)y when transformed to linear form becomes

A function y = f(x) satisfies the differential (dy)/(dx)*sin x -y cos x+sin^2 x/x^2=0 such that y -> 0 as x -> oo . Then:

Find (dy)/(dx) if y= cos^2x

If y = sqrt(sin x + sqrt(sin x + sqrt(sin x + ........... "to " oo))) , then prove that (dy)/(dx) = (cos x)/(2y-1)

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