Evaluate : D Y D X = X + Y + 2 2 ( X + V ) − 1 - Mathematics

Sum

Solve the differential equation  dy/dx = (x + y+2)/(2(x+y)-1)

Solution

dy/dx = ((x+y)+2)/(2(x+y)-1)
Let  x+y=t

1+ dy/dx =dt/dx  rArr dy/dx = dt/dx-1

dt/dx-1= (t+2)/(2t-1)

dt/dx =(t+2)/(2t-1)+1

(dt)/dx = (t+2+2t-1)/(2t-1)

dt/dx=(3t+1)/(2t-1)

((2t-1)/(3t+1))dt = dx

2/3 int (6t -3)/(6t+2)dt=int dx

2/3 int((6t+2)-5)/((6t+2)) dt = x+C_1

2/3 int dt - 10/3 int dt/(6t + 2)=x+C_1

2/3t - 5/3 xx(In|3t+ 1|)/3 = x + C

2/3t - 5/9 xx(In|3t+ 1|) = x + C

2/3(x+y)-5/9In|3(x+y)+1|=x+C

2/3(x+y)- 5/9 In|3x +3y +1|=x+C

Concept: Introduction of Relations and Functions
Is there an error in this question or solution?