CSIR UGC NET Physical Science June 2019 Probability & differential equation

the two problems solved here goes something like this.
In the following circuit each device D may be an insulator with probability p or a conductor with probability 1 – p.
The probability that a non zero current flows through the circuit is

The second problem goes like this:
The solution of the differential equation

with boundary condition y(x=1)=0 is

Solution is below

The Slides can be found here

Csr ugc net phy june19 physics q(10 11 of 55) solution from Bibhatsu Bibhatsu