Question

Find the differential equation dy/dx=sin(x+y)+cos(x+y)

Answer 1

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

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

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

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

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