Solve the following differential equations using the separation of variables. Provide the IMPLICIT solution as final answer unless EXPLICIT solution is required. (1) y' = x(1 + y2); Provide the EXPLCIT solution as final answer (2) (sin x) (sin y) + (cosy) dy = 0; dx (3) (In y)dy + x2y dx = 0; (4) (2a2 - r2) dr = 3 sin 0 do (5) ye2xdx = (4 + e2x)dy = 0