WBJEE2020MathematicsDifferential EquationsActual
Let f be a differentiable function with _ x f(x)=0 . If y^ +y f^ (x)-f(x) f^ (x)=0, _ x y(x)=0 , then ( . where .y^ = d y d x )
Options
- Ay+1=e^ f(x) +f(x)
- By-1=e^ f(x) +f(x)
- Cy+1=e^ -f(x) +f(x)
- Dy-1=e^ -f f] x +f(x)
Correct answer
C. y+1=e^ -f(x) +f(x)
Step-by-step solution
Hint: d y d x +f^ (x) y=f^ (x) f(x) y e^ f(x) = f^ (x) f(x) e^ f(x) d x y e^ f(x) =e^ f(x) (f(x)-1)+c [ Putting f(x)=0 ; y=0, c=1] y e^ f(x) =e^ f(x) (f(x)-1)+1 y=f(x)-1+e^ -f(x) y+1=e^ -f(x) +f(x)