= Consider the initial value problem (2xy² D. + cos x cosy (a) Check whether the differential equation is OA. Separable B. Not exact C. O C. OD. cosy) dx + (2x²y- sin x siny) dy = 0 and y(0) = 1 Exact because (2xy² + cos x cos Exact because (2xy² 3 (b) The general solution of the differential equation is given by A. None of the given answers is correct B. 22 x²y² + sinx siny cos x cos y = C with C an arbirary constant 4xy + sin x siny = C with C an arbirary constant 2xy 3 B. + 3 2x y 3 osy), = (2x²y- sinx siny), os y) = (2x²y- sin x siny) y X + cos x COS OC. 2xy + 2x 3 22 OE. x²y²+ sin x cos y = C with C an arbirary constant X 22 x y + sin x cos y = 0 3 3y + sin x sin y cos x cos y = C with C an arbirary constant (c) The solution of the initial value problem is given implicitly by 22 x y + sin x siny- cos x cos y = - cos 1 www + sin x sin y cos x cos y = - cos 1 -