engineering recuitment GATE ECE 2023-24 Test Series Engineering Mathematics Differential Equations Partial Differential Equations
Consider the following partial differential equation (PDE)
\(\rm a\frac{\partial^2f(x,y)}{\partial x^2}+b\frac{\partial^2f(x,y)}{\partial y^2}=f(x,y)\)
where a and b are distinct positive real numbers. Select the combination(s) of values of the real parameters 𝜉 and 𝜂 such that f(x, y) = e(ξx + ny) is a solution of the given PDF.
1
\(\xi=\frac{1}{\sqrt{2a}}, \eta=\frac{1}{\sqrt{2b}}\)
2
\(\xi=\frac{1}{\sqrt{a}}, \eta=0\)
3
ξ = 0, η = 0
4
\(\xi=\frac{1}{\sqrt{a}}, \eta=\frac{1}{\sqrt{b}}\)