#### 4.16 Problems 751 to 800

4.16.2 $$y'(x)^2=a x^n$$
4.16.3 $$y'(x)^2=y(x)$$
4.16.4 $$y'(x)^2=x-y(x)$$
4.16.5 $$y'(x)^2=x^2+y(x)$$
4.16.6 $$x^2+y'(x)^2=4 y(x)$$
4.16.7 $$3 x^2+y'(x)^2=8 y(x)$$

4.16.9 $$y'(x)^2=y(x)^2+1$$
4.16.10 $$y'(x)^2=1-y(x)^2$$
4.16.11 $$y'(x)^2=a^2-y(x)^2$$
4.16.12 $$y'(x)^2=a^2 y(x)^2$$
4.16.13 $$y'(x)^2=a+b y(x)^2$$
4.16.14 $$y'(x)^2=x^2 y(x)^2$$
4.16.15 $$y'(x)^2=(y(x)-1) y(x)^2$$

4.16.17 $$y'(x)^2=a^2 y(x)^n$$

4.16.26 $$y'(x)^2+2 y'(x)+x=0$$

4.16.28 $$y'(x)^2-2 y'(x)-y(x)^2=0$$
4.16.29 $$y'(x)^2-5 y'(x)+6=0$$
4.16.30 $$y'(x)^2-7 y'(x)+12=0$$
4.16.31 $$a y'(x)+b+y'(x)^2=0$$
4.16.32 $$a y'(x)+b x+y'(x)^2=0$$
4.16.33 $$a y'(x)+b y(x)+y'(x)^2=0$$
4.16.34 $$y'(x)^2+x y'(x)+1=0$$
4.16.35 $$y'(x)^2+x y'(x)-y(x)=0$$
4.16.36 $$y'(x)^2-x y'(x)+y(x)=0$$
4.16.37 $$y'(x)^2-x y'(x)-y(x)=0$$
4.16.38 $$y'(x)^2+x y'(x)-y(x)+x=0$$

4.16.43 $$y'(x)^2-2 x y'(x)+1=0$$

4.16.45 $$y'(x)^2+2 x y'(x)-y(x)=0$$
4.16.46 $$y'(x)^2+2 x y'(x)-y(x)=0$$

4.16.50 $$y'(x)^2+3 x y'(x)-y(x)=0$$