TYPE–3 : (dy/dx) = f (ax+by+c) b ¹ 0
To slove this , substitute t = ax + by + c. Then the equation reduces to separable type in the variable t and x which can be sloved.
Example :
(i) (x + y)2 (dy/dx)=a2.
(ii) sin-1(dy/dx)=x+y
(iii) Ö(1+x+y)(dy/dx)=x+y-1 (put x + y + 1 = t2)
(iv) Find the curve passing through the origin in the form y = f (x) and satisfying the differential equation (dy/dx) = cos (10x+8y)
(v) (dy/dx) =(2x+3y-1)/(4x+6y-5)
