Question 1 [7] Check whether the given function y = (x) is a solution of the given o.d.e: 1.1. 0(x) = =; ( x' + 1)y+y+1=0 (3 ) 1.2. p(x) = xe3x. dy -9dy -= 603x dx2 dx (4) Question 2 [19] 2.1.Solve the differential equation (1 + x2) 2 + xy = 0 and determine the particular solution when y(0) = 2, expressing y in terms of x. (5) 2.2.Show that the following differential equation y = xe"* is separable and find the general solution, expressing y in terms of x (6) 2.3. Use the substitution y = tx to solve (x -2x) + 2x* -y' + 4x'y)dx + (xy? -4x3)dy =0 (8) Question 3 [6] 3.1.Find the general solution of y + 2xy = x and find the particular solution that satisfies y(0) = 2 (3) 3.2. Solve the initial value problem xy -2y =3x , y(-1) =2 (3) Question 4 [8] Find the general solution of the given differential equations: 4.1. y +8y +16y=0 (3) Solve the given differential equation subjects to the indicated initial conditions: 4.2. y +4y=0; y(0) =4 y (0) =6