• If the initial condition is greater than b/2

V will decrease until reach b/2 see Fig 1 in the attached file.

• If the initial condition is less than b/2  but away from 0 from  right

V will increase until reach b/2 see Fig 2 in the attached file.

• If the initial condition is less than b/2  and near 0 from right and left

You can’t detect the output practically but theoretically if v near 0 from right, v must increase dramatically until reach b/2 and if v near 0 from left, v must decrease dramatically until certain point and then decrease linearly with time.

• If the initial condition is less than 0  but away from 0

V will decrease linearly with time as t increase Fig 3 in the attached file.

Hello Jayachander Rao,

What about P2(x) and Q2(x)?

The constants, am I free to take  any value?

If I Solve it, I'll give you semianalytic solution.

See the attached file.

I can reduce the error much more.

this solution is not  numerical solution, it is semi analytic.

I have a general approximate analytic form which can be applied  to intervals between points.

See this:

https://www.researchgate.net/publication/265162885_INTRODUCTION_TO_PIECEWISE_ANALYTIC_METHOD

https://www.researchgate.net/publication/274470344_Piecewise_Analytic_Method_Solving_Any_Nonlinear_Ordinary_Differential_Equation_of_1st_Order_with_Any_Initial_Condition

https://www.researchgate.net/publication/265162885_INTRODUCTION_TO_PIECEWISE_ANALYTIC_METHOD

Conference Paper INTRODUCTION TO PIECEWISE ANALYTIC METHOD

Article Piecewise Analytic Method (Solving Any Nonlinear Ordinary Di...

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Piecewise Analytic Method (PAM) is a New Step in the Evolution of Solving Nonlinear Differential Equation