Teaching CSIR NET Mock Test Series Mathematical Science Partial Differential Equations PDE With Constant Coefficient
Consider the Cauchy problem
\(\left\{\begin{array}{c} \frac{\partial^2 u}{\partial x \partial y}=0,|x|<1,0
Which of the following statements are true?
1
A necessary condition for a solution to exist is that g is an odd function
2
A necessary condition for a solution to exist is that g is an even function
3
The solution (if it exists) is given by \(u(x, y)=2 \int_x^{\sqrt{y}} z g(z) d z\)
4
The solution (if it exists) is given by \(u(x, y)=2 \int_{\sqrt{y}}^{x^2} z g(z) d z\)