99 Percentile Qs Bank for JEE MainMathematicsDifferential Equations
The general solution of the differential equation d y d x = (x-y)+ (x-y) is
Options
- A| (x-y) 2 +1 (x-y) 2 |=x+c
- B| (x-y) 2 -1 (x-y) 2 |=x+c
- C| (x-y)-1 (x-y) |=x+c
- D| (x-y)+ (x-y) (x-y) |=x+c
Correct answer
B. | (x-y) 2 -1 (x-y) 2 |=x+c
Step-by-step solution
d y d x = (x-y)+ (x-y) Put x-y=v aligned & 1- d y d x = d v d x & 1- d v d x = v+ v & 1-( v+ v)= d v d x & d v 1-( v+ v) =d x & d v 1- 2 v 2 1+ ^2 v 2 - 1- ^2 v 2 1+ ^2 v 2 =d x & (1+ ^2 v 2 ) d v 1+ ^2 v 2 -2 v 2 -1+ ^2 v 2 =d x & ^2 v 2 d v 2 ^2 v 2 -2 v 2 =d x & aligned Let v 2 =u 1 2 ^2 v 2 d v=d u aligned & d u u^2-u =d x d u u(u-1) =d x & ( -1 u + 1 u-1 ) d u= d x & x+C= |u-1|- |u| & x+C= | v 2 -1 |- | v 2 | aligned x+C= | x-y 2 -1 x-y 2 |