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KCET2021MathematicsDifferential Equations

The number of solutions of d y d x = y+1 x-1 , when y( l )=2 is

Options

  1. Athree
  2. Bone
  3. Cinfinite
  4. Dtwo

Correct answer

B. one

Step-by-step solution

d y d x = y+1 x-1 1 x-1 d x= 1 y+1 d y Integrating both sides, 1 x-1 d x= 1 y+1 d y |x-1|= |y+1|+ C (x-1)=c(y+1) As, y(1)=2 , 0=c(3) c=0 Hence, x-1=0 or x=1 The given differential equation has only one solution.

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