4.18 Problems 851 to 900

   4.18.1 \(x y'(x)^2+y'(x)=y(x)\)
   4.18.2 \(x y'(x)^2+2 y'(x)-y(x)=0\)
   4.18.3 \(x y'(x)^2-2 y'(x)-y(x)=0\)
   4.18.4 \(x y'(x)^2+4 y'(x)-2 y(x)=0\)
   4.18.5 \(x y'(x)^2+x y'(x)-y(x)=0\)
   4.18.6 \(-\left (x^2+1\right ) y'(x)+x y'(x)^2+x=0\)
   4.18.7 \(a+x y'(x)^2+y(x) y'(x)=0\)
   4.18.8 \(a+x y'(x)^2-y(x) y'(x)=0\)
   4.18.9 \(a x+x y'(x)^2-y(x) y'(x)=0\)
   4.18.10 \(-x^2+x y'(x)^2+y(x) y'(x)=0\)
   4.18.11 \(x^3+x y'(x)^2+y(x) y'(x)=0\)
   4.18.12 \(a y(x)+x y'(x)^2-y(x) y'(x)=0\)
   4.18.13 \(y(x) y'(x)+x y'(x)^2-y(x)^4=0\)
   4.18.14 \((a-y(x)) y'(x)+b+x y'(x)^2=0\)
   4.18.15 \(x y'(x)^2+(x-y(x)) y'(x)-y(x)+1=0\)
   4.18.16 \((a-y(x)+x) y'(x)+x y'(x)^2-y(x)=0\)
   4.18.17 \(x y'(x)^2-(3 x-y(x)) y'(x)+y(x)=0\)
   4.18.18 \(a-b y(x)+b x+x y'(x)^2-y(x)=0\)
   4.18.19 \(a+x y'(x)^2-2 y(x) y'(x)=0\)
   4.18.20 \(x y'(x)^2+2 y(x) y'(x)-x=0\)
   4.18.21 \(a x+x y'(x)^2-2 y(x) y'(x)=0\)
   4.18.22 \(x y'(x)^2-2 y(x) y'(x)+2 y(x)+x=0\)
   4.18.23 \(9 x^2+x y'(x)^2-3 y(x) y'(x)=0\)
   4.18.24 \(x y'(x)^2-(3 y(x)+2 x) y'(x)+6 y(x)=0\)
   4.18.25 \(-a y(x) y'(x)+b+x y'(x)^2=0\)
   4.18.26 \(a y(x) y'(x)+b x+x y'(x)^2=0\)
   4.18.27 \(x y'(x)^2-(x y(x)+1) y'(x)+y(x)=0\)
   4.18.28 \((1-x) y(x) y'(x)+x y'(x)^2-y(x)^2=0\)
   4.18.29 \(\left (1-x^2 y(x)\right ) y'(x)+x y'(x)^2-x y(x)=0\)
   4.18.30 \((x+1) y'(x)^2=y(x)\)
   4.18.31 \((x+1) y'(x)^2-(y(x)+x) y'(x)+y(x)=0\)
   4.18.32 \((a-x) y'(x)^2-b+y(x) y'(x)=0\)
   4.18.33 \((a+x) y'(x)^2+y'(x) (\text {a1}+\text {b1} x+\text {c1} y(x))+\text {a2}+\text {b2} x+\text {c2} y(x)=0\)
   4.18.34 \(2 x y'(x)^2+(2 x-y(x)) y'(x)-y(x)+1=0\)
   4.18.35 \(3 x y'(x)^2-6 y(x) y'(x)+2 y(x)+x=0\)
   4.18.36 \((3 x+1) y'(x)^2-3 (y(x)+2) y'(x)+9=0\)
   4.18.37 \((3 x+5) y'(x)^2-(3 y(x)+3) y'(x)+y(x)=0\)
   4.18.38 \(4 x y'(x)^2=(a-3 x)^2\)
   4.18.39 \(4 x y'(x)^2+2 x y'(x)-y(x)=0\)
   4.18.40 \(4 x y'(x)^2-3 y(x) y'(x)+3=0\)
   4.18.41 \(4 x y'(x)^2+4 y(x) y'(x)=1\)
   4.18.42 \(4 y(x) y'(x)+4 x y'(x)^2-y(x)^4=0\)
   4.18.43 \(4 (2-x) y'(x)^2+1=0\)
   4.18.44 \(8 y(x) y'(x)+16 x y'(x)^2+y(x)^6=0\)
   4.18.45 \(x^2 y'(x)^2=a^2\)
   4.18.46 \(x^2 y'(x)^2=y(x)^2\)
   4.18.47 \(x^2 y'(x)^2+x^2-y(x)^2=0\)
   4.18.48 \(x^2 y'(x)^2=(x-y(x))^2\)
   4.18.49 \(x^2 y'(x)^2-y(x)^4+y(x)^2=0\)
   4.18.50 \(x^2 y'(x)^2-x y'(x)+(1-y(x)) y(x)=0\)