MathProblemsBank

2.2.1 Derivatives and differentials

Problem: Check that function \( U=\ln \frac{1}{\sqrt{x^{2}+y^{2}}} \) is a solution to the partial differential equation \( \frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=0 \).