Consider the following differential equations. x = 4y², x(7) = 1 P(y) = dx Find the coefficient function P(y) when the given differential equation is written in the standard form + P(y)x = f(y). dy у e/P(y)dy = = dx dy 1 y Find the integrating factor for the differential equation. 1 y Solve the given initial-value problem. x(y) = 4y²- 195 y 7 Give the largest interval I over which the solution is defined. (Enter your answer using interval notation.) 1 = (-∞,0) U (0,0)

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