\magnification 2200
\parindent 0pt
\parskip 10pt
\pageno=1
\hsize 7truein
\vsize 9.2truein
\def\u{\vskip -10pt}
\def\v{\vskip -6pt}

Thm 2.4.2:  Suppose $f, {\partial f \over \partial y}: (a, b) \times (c, d)$ are continuous on $(a, b) 
\times (c, d)$ and the      
point $(t_0, y_0) \in (a, b) \times (c, d)$, then there exists an interval $(t_0 - h, t_0 + h) \subset 
(a, b) such that here exists a unique function $y = \phi(t)$ that satisfies the following
initial value problem:  $$y'  = f(t, y), $$y(t_0) = y_0.$$

Thm 2.4.1:  If $p$ and $g$ are continuous on $(a, b)$ and the
point $t_0 \in (a, b)$, then there exists a unique function $y = \phi(t)$ that satisfies the following 
initial value problem:  $$y' + p(t)y = g(t), y(t_0) = y_0.$$

\vskip 10pt
\hrule

2.4 \#27b.  Solve Bernoulli's equation, $$y' + p(t)y = g(t)y^n,$$ when $n > 1$ by changing it 
to a linear equation ny 
substituting $v = y^{1-n}$

\vskip 10pt
\hrule

Solve 

$$ty' + 2t^{-2}y = 2t^{-2}y^5,$$


\end