Suppose I want to solve a 1st order linear PDE $$xu_x-yu_y=0,\qquad u(x,0)=f(x)$$ The solution obtained from Lagrange's equation is $u(x,y)=f(y/x)$. Here the characteristics look like rectangular hyperbola. How do I look at this pde from the geometric viewpoint so that I can get an intuitive picture of the solution by inspection without actually solving the pde ?
2026-03-27 17:33:15.1774632795
Solving a PDE geometrically
126 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in GEOMETRY
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