MHT CET202123 Sep 2021Evening ShiftMathematicsDifferential EquationsActual
The general solution of the differential equation d y d x =2^ y-x is
Options
- A2^x-2^y=c
- B1 2^x - 1 2^y =c
- C1 2^x + 1 2^y =c
- D2^x+2^y=c
Correct answer
B. 1 2^x - 1 2^y =c
Step-by-step solution
aligned & d y d x =2^ y-x & d y d x = 2^y 2^x d y 2^y = d x 2^x & 2^ -y d y= 2^ -x d x 2^ -y - n 2 = 2^ -x - 2 +c₁ 2^ -y 2 = 2^ -x 2 -c₁ & 1 2 [2^ -x -2^ -y ]=c₁ & 1 2^x - 1 2^y =c, where c= (c₁ )( 2) aligned