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Differential EquationsEasyExistence, Uniqueness & Bifurcations

Existence, Uniqueness & Bifurcations · Easy problem

Apply one step of Picard iteration to y′=2t−yy' = 2t - y, y(0)=1y(0) = 1, starting from φ0(t)=1\varphi_0(t) = 1 and using φ1(t)=1+∫0t(2s−φ0(s)) ds\varphi_1(t) = 1 + \displaystyle\int_0^t \big(2s - \varphi_0(s)\big)\,ds. Evaluate φ1(3)\varphi_1(3).