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Differential EquationsSuperchallengeExact Equations & Substitutions

Exact Equations & Substitutions · Superchallenge problem

The Riccati equation y′=e−xy2+y−exy' = e^{-x}y^2 + y - e^x has a particular solution of the form y=ekxy = e^{kx}. Use it to solve the equation with y(0)=2y(0) = 2, and find y(−ln⁡3)y(-\ln 3).