State a region in the r-y-plane, where the hypotheses of Picard's theorem (namely: continuity of f(x,...

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State a region in the r-y-plane, where the hypotheses of Picard's theorem (namely: continuity of f(x, y) and Of(x, y)/Oy) are satisfied and that contains the initial point (ro. yo). Thus, Picard's theorem allows you to conclude that there exists a unique solution through each given initial point in this region. x-y y(0) = 1 2x + 5y (b) y'= (1-2² - y²)¹/2, y(0) = 0 (c) y'= 3(x+y)-², y(0) = -1 (d) y(1)=2 (a) y'= (e) = dy dr In ry 1-x² + y²¹ 11 (f) = dr 1+z² 3y-y² (cot(x))y 1+y y(0) = 1 y(π/2) = 0 State a region in the r-y-plane, where the hypotheses of Picard's theorem (namely: continuity of f(x, y) and Of(x, y)/Oy) are satisfied and that contains the initial point (ro. yo). Thus, Picard's theorem allows you to conclude that there exists a unique solution through each given initial point in this region. x-y y(0) = 1 2x + 5y (b) y'= (1-2² - y²)¹/2, y(0) = 0 (c) y'= 3(x+y)-², y(0) = -1 (d) y(1)=2 (a) y'= (e) = dy dr In ry 1-x² + y²¹ 11 (f) = dr 1+z² 3y-y² (cot(x))y 1+y y(0) = 1 y(π/2) = 0