The discussion focuses on solving the non-linear ordinary differential equation (ODE) given by (x*y'')^2 - (1 + (y')^2) = 0. Participants suggest substituting u = y' to transform the equation into a pair of first-order separable equations: (x*u')^2 - (1 + u^2) = 0 and xu' = ±√(1 + u^2). This substitution simplifies the problem and allows for analytical solutions to be pursued more effectively.
PREREQUISITESMathematicians, physics students, and engineers interested in solving non-linear ordinary differential equations and understanding pursuit curves in dynamic systems.
abercrombiems02 said:How would one go about finding an analytical solution to the following ODE
note that we are trying to find y(x) subject to...
(x*y'')^2 - (1 + (y')^2) = 0