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SSC Applied Mathematics QUESTION #1316
Question 1
The boundary value problem \(u_{xx}+u_{yy}=0\) with \(u=0\) on three sides and \(u(x,b)=f(x)\) is solved by the method of:
  • Finite differences
  • Separation of variables✔️
  • Euler's method
  • Newton-Raphson
Correct Answer Explanation
The Laplace equation \(u_{xx}+u_{yy}=0\) on a rectangle with homogeneous Dirichlet conditions on three sides is a classic problem solved by separation of variables. Assuming \(u(x,y)=X(x)Y(y)\) and applying boundary conditions leads to a Fourier sine series solution.