Consider the differential equation

\(\frac{dy}{dx}=y^2,(x,y)\in\mathbb{R}\times\mathbb{R}\)

Then

(a) all solutions of the differential equation are defined on \((-\infty,\infty)\).

(b) no solution of the differential equation are defined on \((-\infty,\infty)\).

(c) the solution of the differential equation satisfying the initial condition \(y(x_0)=y_0,y_0>0,\)is defined on \((-\infty,x_0+\frac{1}{y_0})\)

(d) the solution of the differential equation satisfying the initial condition \(y(x_0)=y_0,y_0>0\), is defined on \((x_0-\frac{1}{y_0},\infty)\).

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