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

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)

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

(dy)/(dx)tany=sin(x+y)+sin(x-y)

Solve the following differential equations (x cos\ (y)/(x)+y sin\ (y)/(x))y\ dx=(ysin\ (y)/(x)-xcos\ (y)/(x))x\ dy

The solution of differential equation (x+y(dy)/(dx))/(y-x(dy)/(dx)) = x(cos^(2)(x^(2)+y^(2))/(y^(3))) is

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

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

Solve: (i) sin^(-1)((dy)/(dx))=x+y (ii) (dy)/(dx)=cos(x+y) (iii) (dy)/(dx)=(4x+y+1)^2

Suppose cos^(2)y.(dy)/(dx)=sin(x+y)+sin(x-y), |x| le (pi)/(2) and |y|le(pi)/(2). If y((pi)/(3))=-(pi)/(2), then y((pi)/(2)) is

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