Test 1 Engineering Mathematics 03 SOSE Manipal International University Nilai, Negeri Sembilan, Malaysia Answer all Questions. dy/dx + xy = x + = 0, 0 0 ii. b. Solve the potential equation, u(0,y) = 0 and ux(1,y) = 0, 0 < x < 1 and, u(x,0) = 0 and (x,1) = sin x, 0 < y < 1 y-3, x > 0 Hint: Use substitution x = yn chose proper for I and ii. b. Solve the 2nd ODE, i. d2y/dt2 + 4y = sin 2t by a. finding yh(t) and yp(t) b. Laplace Transform Q1.3 Show that, u(x,y) = (1/2) [f(x - ct) + g(x + ct)] is a solution to the wave equation, , t > 0. 0 < x < 1 Q2.1 a. Solve the heat equation, , 0 < x < 1. T >0 With, u(0,t) = 0 and ux(1,t) =0, t >0 u(x,0) = x, 0 < x < 0 Prof amer/2017/manipal