MATH 3D Study Guide - Midterm Guide: Singular Solution, Damping Ratio, Equilibrium Point
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Total marks = 50 (per question in brackets) Unless otherwise stated, include all your working for full credit. Try all parts of every question, even if you can"t do the rst part! Total: solve the following linear initial value problems: + 2xy = e x2 (a) dx y(0) = 1 (5) Y(cid:48)(cid:48) + 5y(cid:48) + 4y = 0 y(0) = 3 y(cid:48)(0) = 6 (b) (5) 2. (a) what is meant by the term singular solution? (b) find all the solutions to the following ode: = x2(y 1)(y + 2) dy dx (give your answer in the form y(x) = and be sure to include all solutions. (2) (8: consider the following matrix ode: Each month they add or remove sh in proportion to how far the population is from 100. The new popula- tion may therefore be modelled by dp dt. 100 (p 100)(p 50) + k(100 p) where k is a positive constant.
