If (dy/dx)= xcos(x^2) and y = -3 when x = 0, then when x = π, y = a.) -3.215 b.) √2 c.) 1.647 d.) 6 e.) 3π

The answer is  -3.215======this is a separable differential equation problem. it gives us an initial value to work worth, meaning we have to find a specific solution to the differential equation. then we use that solution curve to find the value of y at x =  π    move the differential dx to the right-hand side since all the x-terms are there.    integrate both sides of the equation.    using substitution for the right-hand-side integral, we let u = x². thus simple differentiation gives us    so substituting it into the integral, we get    solve for c using initial condition: "y = -3 when x = 0"    therefore, the specific solution curve is  . when evaluated at x =  π, we get a y-value of    the answer is  -3.215