4.20 Problems 951 to 1000

   4.20.1 \(-(a-2 b x) y'(x)-b y(x)+y(x) y'(x)^2=0\)
   4.20.2 \(x^3 y'(x)-x^2 y(x)+y(x) y'(x)^2=0\)
   4.20.3 \(y(x) y'(x)^2+(x-y(x)) y'(x)-x=0\)
   4.20.4 \(y(x) y'(x)^2-(y(x)+x) y'(x)+y(x)=0\)
   4.20.5 \(y(x) y'(x)^2-(x y(x)+1) y'(x)+x=0\)
   4.20.6 \(y(x) y'(x)^2+\left (x-y(x)^2\right ) y'(x)-x y(x)=0\)
   4.20.7 \(y(x) y'(x)^2+y(x)=a\)
   4.20.8 \((y(x)+x) y'(x)^2+2 x y'(x)-y(x)=0\)
   4.20.9 \((2 x-y(x)) y'(x)^2-2 (1-x) y'(x)-y(x)+2=0\)
   4.20.10 \(2 y(x) y'(x)^2+(5-4 x) y'(x)+2 y(x)=0\)
   4.20.11 \(4 x^3 y'(x)-4 x^2 y(x)+9 y(x) y'(x)^2=0\)
   4.20.12 \((1-a y(x)) y'(x)^2=a y(x)\)
   4.20.13 \(y'(x)^2 (\text {a0}+\text {b0} x+\text {c0} y(x))+y'(x) (\text {a1}+\text {b1} x+\text {c1} y(x))+\text {a2}+\text {b2} x+\text {c2} y(x)=0\)
   4.20.14 \(\left (x^2-a y(x)\right ) y'(x)^2-2 x y(x) y'(x)=0\)
   4.20.15 \(x y(x) y'(x)^2+(y(x)+x) y'(x)+1=0\)
   4.20.16 \(\left (x^2+y(x)^2\right ) y'(x)+x y(x) y'(x)^2+x y(x)=0\)
   4.20.17 \(\left (x^2-y(x)^2\right ) y'(x)+x y(x) y'(x)^2-x y(x)=0\)
   4.20.18 \(-\left (x^2-y(x)^2\right ) y'(x)+x y(x) y'(x)^2-x y(x)=0\)
   4.20.19 \(\left (a+x^2-y(x)^2\right ) y'(x)+x y(x) y'(x)^2-x y(x)=0\)
   4.20.20 \(-y'(x) \left (a-b x^2+y(x)^2\right )-b x y(x)+x y(x) y'(x)^2=0\)
   4.20.21 \(\left (3 x^2-2 y(x)^2\right ) y'(x)+x y(x) y'(x)^2-6 x y(x)=0\)
   4.20.22 \(-2 x y(x) y'(x)+x (x-2 y(x)) y'(x)^2+y(x)^2-2 x y(x)=0\)
   4.20.23 \(6 x y(x) y'(x)+x (x-2 y(x)) y'(x)^2+y(x)^2-2 x y(x)=0\)
   4.20.24 \(y(x)^2 y'(x)^2=a^2\)
   4.20.25 \(-a^2+y(x)^2 y'(x)^2+y(x)^2=0\)
   4.20.26 \(y(x)^2 y'(x)^2-3 x y'(x)+y(x)=0\)
   4.20.27 \(-6 x^3 y'(x)+4 x^2 y(x)+y(x)^2 y'(x)^2=0\)
   4.20.28 \(4 a^2-4 a y(x) y'(x)-4 a x+y(x)^2 y'(x)^2+y(x)^2=0\)
   4.20.29 \(y(x)^2 y'(x)^2-(x+1) y(x) y'(x)+x=0\)
   4.20.30 \(x^2+2 x y(x) y'(x)+y(x)^2 y'(x)^2=0\)
   4.20.31 \(a+y(x)^2 y'(x)^2+2 x y(x) y'(x)-y(x)^2=0\)
   4.20.32 \(-x^2-2 x y(x) y'(x)+y(x)^2 y'(x)^2+2 y(x)^2=0\)
   4.20.33 \(a-x^2-2 x y(x) y'(x)+y(x)^2 y'(x)^2+2 y(x)^2=0\)
   4.20.34 \((a-1) b+a x^2+2 a x y(x) y'(x)+(1-a) y(x)^2+y(x)^2 y'(x)^2=0\)
   4.20.35 \(\left (1-y(x)^2\right ) y'(x)^2=1\)
   4.20.36 \(\left (a^2-y(x)^2\right ) y'(x)^2=y(x)^2\)
   4.20.37 \(\left (a^2-2 a x y(x)+y(x)^2\right ) y'(x)^2+2 a y(x) y'(x)+y(x)^2=0\)
   4.20.38 \(\left (a^2 x^2-y(x)^2\right ) y'(x)^2+\left (a^2-1\right ) x^2-2 x y(x) y'(x)=0\)
   4.20.39 \(\left ((1-a) x^2+y(x)^2\right ) y'(x)^2+2 a x y(x) y'(x)+(1-a) y(x)^2+x^2=0\)
   4.20.40 \(\left (\left (1-4 a^2\right ) x^2+y(x)^2\right ) y'(x)^2-8 a^2 x y(x) y'(x)+\left (1-4 a^2\right ) y(x)^2+x^2=0\)
   4.20.41 \(\left (\left (1-a^2\right ) x^2+y(x)^2\right ) y'(x)^2+2 a^2 x y(x) y'(x)+\left (1-a^2\right ) y(x)^2+x^2=0\)
   4.20.42 \((y(x)+x)^2 y'(x)^2=y(x)^2\)
   4.20.43 \(-\left (x^2-x y(x)-2 y(x)^2\right ) y'(x)+(y(x)+x)^2 y'(x)^2-(x-y(x)) y(x)=0\)
   4.20.44 \(2 a^2 y'(x)+\left (a^2-(x-y(x))^2\right ) y'(x)^2+a^2-(x-y(x))^2=0\)
   4.20.45 \(x^2+2 x y(x) y'(x)+2 y(x)^2 y'(x)^2+y(x)^2-1=0\)
   4.20.46 \(-x^2-2 x y(x) y'(x)+3 y(x)^2 y'(x)^2+4 y(x)^2=0\)
   4.20.47 \(3 x^3+2 (3 x+1) x y(x) y'(x)+4 y(x)^2 y'(x)^2=0\)
   4.20.48 \(\left (x^2-4 y(x)^2\right ) y'(x)^2-4 x^2+6 x y(x) y'(x)+y(x)^2=0\)
   4.20.49 \(9 y(x)^2 y'(x)^2-3 x y'(x)+y(x)=0\)
   4.20.50 \((2-3 y(x))^2 y'(x)^2=4 (1-y(x))\)