BITSAT Mathematics Question (2024) — Solution

Step-by-step solution

d y d x -y _e 2=2^ x ( x-1) _e 2 This is linear differential equation I.F. =e^ - _e 2 d x =e^ -x _e 2 =2^ -x then general Solution is y 2^ -x = 2^ -x 2^ x ( x-1) _e 2 d x+c Now let x-x=t ( x-1) d x=d t aligned & y 2^ -x = _e 2 2^t d t+c \\ & y 2^ -x =2^t+c \\ & y=2^ x+t +c 2^x \\ & y=2^ x +c 2^x aligned