(a). If 2xy³ +3y cos(xy)+(cx²y² +3x cos(xy))y'=0 is an exact equation, determine the value of c. (b). Use the Test for Exactness to check the differential equation (2x+y³ sec² x)dx+(1+3y² tanx)dy=0. Then, solve the initial value problem when x₁ = π and y₁ = 2. (c). Determine the integrating factor and solve explicitly the linear dy_2y__x² cosx. = differential equation X dx

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