Math Problem Statement
solve the differential equation y*(dy/dx)^2 + 2xdy/dx - y = 0 by change of variable from y, x to r, x, where y^2=r^2-x^2 and y*(dy/dx)=r*(dr/dx)-x. Note that r is a function (not a constant)
Solution
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Substitution Method
Nonlinear Equations
Formulas
y^2 = r^2 - x^2
y (dy/dx) = r (dr/dx) - x
(dy/dx)^2 = ((r dr/dx - x)^2) / (r^2 - x^2)
Theorems
Chain Rule for Differentiation
Methods for Solving First-Order Differential Equations
Suitable Grade Level
Undergraduate Mathematics
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