COMEDK2012MathematicsDifferential Equations
The solution of d y d x -1=e^ x-y is
Options
- Ae^ x-y +x=c
- Be^ -(x-y) +x=c
- Ce^ -(x-y) =x+c
- De^ x-y =x+c
Correct answer
C. e^ -(x-y) =x+c
Step-by-step solution
Given, differential equation is d y d x -1=e^ x-y array lrl Put & & x-y=t & 1- d y d x = d t d x array So, given equation becomes, aligned - d t d x &=e^ t -e^ -t d t &=d x aligned Integrating both sides, we get aligned &e^ -t =x+c &e^ -(x-y) =x+c aligned