MATH 3D Study Guide - Quiz Guide: Product Rule, Integrating Factor
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Math 3d quiz 1 afternoon - january 24th. Please put name on front & id on back for redistribution! *there is a question on the back side: consider the following ode with initial condition: x(cid:48) = e t2 (a) [3pts] prove that this has a unique solution. (hint: section 1. 2 material). and x(0) = 2. x. , fx(t, x) = e t2 x2 , and (t0, x0) = (0, 2): f is continuous as long as x0 is away from 0. You may leave a de nite integral in the answer. Separating, and using leibniz notation, we have that x dx = e t2 dt = xdx = e t2 dt. (cid:90) We cannot nd an antiderivative to e t2 so we have to make it a de nite integral, 2 x2 = c + 2 e s2 ds. (cid:90) (cid:90) (cid:90) t. The initial condition implies ( 2)2 = c + 2 (cid:90) 0.
