Solve each of the following initial value problems

It is a homogeneous equation

Put y = vx

And

So,

…… (a)

Comparing coefficients of like power of v,

A = 1 …… (1)

B + D = 0 …… (2)

– B + C + D = 0 …… (3)

A + B + C = – 2 …… (4)

Solving eq.(1),(2),(3) and (40,We get,

A = 1,B = – 1 C = – 2,D = 1

Using eq. (a)

log v – log (v + 1) – log() = log xc

log () = log xc