\( \frac{d x}{d t}=6 y^{3}, \frac{d y}{d t}=2 y \) Verify that the pair \( x(t)=e^{6 t}, y(t)=e^{2 t} \) is a solution to the given system below. Sketch the trajectory of the given solution in the phase plane. (Type expressions using t as the variable.) A. The pair \( x(t)=e^{6 t}, y(t)=e^{2 t} \) is a solution because in terms of \( t, \int x(t) d t=\square \) and \( \int y(t) d t=\square \). In terms of \( x \) and \( y \), \( \int x(t) d t=\square \) and \( \int y(t) d t=\square \). B. The pair \( x(t)=e^{6 t}, y(t)=e^{2 t} \) is a solution because in terms of \( t, x^{\prime}(t)=\square \) and \( y^{\prime}(t)=\square \). In terms of \( x \) and \( y, x^{\prime}(t)=\square \) and \( y^{\prime}(t)=\square \).
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