Question

What is the complete solution of the equation, \(q= e^\frac{-p}{α}\)?

(a) \(z=ae^\frac{-a}{α} y\)

(b) \(z=x+e^\frac{-a}{α} y\)

(c) \(z=ax+e^\frac{-a}{α} y+c\)

(d) \(z=e^\frac{-a}{α} y\)

I had been asked this question by my college director while I was bunking the class.

My query is from Non-Homogeneous Linear PDE with Constant Coefficient topic in portion Partial Differential Equations of Engineering Mathematics

Answer 1

The correct choice is (c) \(z=ax+e^\frac{-a}{α} y+c\)

Easiest explanation: Given: \(q= e^\frac{-p}{α}\)

The given equation does not contain x, y and z explicitly.

Setting p = a and q = b in the equation, we get \(b= e^\frac{-p}{α}.\)

Hence, a complete solution of the given equation is,

z=ax+by+c, with  \(b= e^\frac{-a}{α}\)

\(z=ax+e^\frac{-a}{α} y+c.\)