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

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