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\begin{document}
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{\newpage
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\samepage \begin{displaymath}y'(t)=g(t)y(t)+h(t)[y(t)]^n \hspace{.2in} (*) 
\end{displaymath}
}

{\newpage
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\samepage \begin{displaymath}v(t)=[y(t)]^{1-n}
\end{displaymath}
}

{\newpage
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\samepage \begin{displaymath}v'(t)=(1-n)[y(t)]^{-n}y'(t)
\end{displaymath}
}

{\newpage
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\samepage \begin{displaymath}y'(t)=\frac{[y(t)]^n}{1-n}v'(t)
\end{displaymath}
}

{\newpage
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\samepage \begin{displaymath}\frac{[y(t)]^n}{1-n}v'(t)=g(t)y(t)+h(t)[y(t)]^n
\end{displaymath}
}

{\newpage
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\samepage \begin{displaymath}v'(t)=(1-n)g(t)[y(t]^{1-n})+(1-n)h(t)
\end{displaymath}
}

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\samepage \begin{displaymath}v'(t)=(1-n)g(t)v(t)+(1-n)h(t) \hspace{.2in} (**)
\end{displaymath}
}

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\samepage \begin{displaymath}y(t)=[v(t)]^{1/(1-n)}
\end{displaymath}
}

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\samepage \begin{displaymath}y'=5y-5ty^3
\end{displaymath}
}

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\samepage \begin{displaymath}v(t)=[y(t)]^{-2}
\end{displaymath}
}

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\samepage \begin{displaymath}v'(t)=-2[y(t)]^{-3}y'(t)
\end{displaymath}
}

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\samepage \begin{displaymath}y'(t)=-\frac{1}{2}[y(t)]^3v'(t)
\end{displaymath}
}

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\samepage \begin{displaymath}-\frac{1}{2}y^3v'=5y-5ty^3
\end{displaymath}
}

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\samepage \begin{displaymath}v'=-\frac{10}{y^2}+10t
\end{displaymath}
}

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\samepage \begin{displaymath}v'=-10v+10t
\end{displaymath}
}

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\samepage \begin{displaymath}v(t)=Ce^{10t}+t-\frac{1}{10},
\end{displaymath}
}

{\newpage
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\samepage \begin{displaymath}y^{-2}=Ce^{10t}+t-\frac{1}{10}
\end{displaymath}
}

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