MT1710 - 2018/19: Question Sheet 11 Not marked but on examinable material! 1. Obtain the general solution of ?2 y + 3- dy + 2y = 10 sin x ; dx2 (a) (b) d2 y dx2 dx d3 y d2 y (c) dx3 dx2 (d) ?2 y dy d23 (e) dx2 + y = x(1 + sin x) . 2. Solve the differential equations dx + 2- dy 3y = 4e" ; 3 + 4y = 6 cosh x ; 2 + 2y = e" sin x ; dx2 dx (a) dx dy __ e-"; (b) 2xy Ax dy _3y2 - x2 dx (c) dy = y + Vx2 + y2, subject to y(1) = 0 ; Hint: In question 2 (c) you may use arcsinh v = ln(v + v1 + v2), to express the solution in a simpler way.