4.17 Problems 801 to 850

   4.17.1 \(y'(x)^2-4 (x+1) y'(x)+4 y(x)=0\)
   4.17.2 \(a x y'(x)+y'(x)^2=b c x^2\)
   4.17.3 \(-a x y'(x)+a y(x)+y'(x)^2=0\)
   4.17.4 \(a x y'(x)+b x^2+c y(x)+y'(x)^2=0\)
   4.17.5 \((a+b x) y'(x)+c+y'(x)^2=b y(x)\)
   4.17.6 \(-2 x^2 y'(x)+2 x y'(x)+y'(x)^2=0\)
   4.17.7 \(a x^2 y'(x)+b x y(x)+y'(x)^2=0\)
   4.17.8 \(a x^3 y'(x)-2 a x^2 y(x)+y'(x)^2=0\)
   4.17.9 \(-2 a x^3 y'(x)+4 a x^2 y(x)+y'(x)^2=0\)
   4.17.10 \(4 x^5 y'(x)-12 x^4 y(x)+y'(x)^2=0\)
   4.17.11 \(y'(x)^2-2 \cosh (x) y'(x)+1=0\)
   4.17.12 \(y'(x)^2+y(x) y'(x)=x (y(x)+x)\)
   4.17.13 \(y'(x)^2-y(x) y'(x)+e^x=0\)
   4.17.14 \(y'(x)^2+(y(x)+x) y'(x)+x y(x)=0\)
   4.17.15 \(y'(x)^2-2 y(x) y'(x)-2 x=0\)
   4.17.16 \(y'(x)^2+(2 y(x)+1) y'(x)+(y(x)-1) y(x)=0\)
   4.17.17 \(y'(x)^2-2 (x-y(x)) y'(x)-4 x y(x)=0\)
   4.17.18 \(y'(x)^2-(4 y(x)+1) y'(x)+y(x) (4 y(x)+1)=0\)
   4.17.19 \(y'(x)^2-2 (1-3 y(x)) y'(x)-(4-9 y(x)) y(x)=0\)
   4.17.20 \(y(x) (3 a+b+9 y(x))+(a+6 y(x)) y'(x)+y'(x)^2=0\)
   4.17.21 \(a y(x) y'(x)-a x+y'(x)^2=0\)
   4.17.22 \(-a y(x) y'(x)-a x+y'(x)^2=0\)
   4.17.23 \(y'(x) (a x+b y(x))+a b x y(x)+y'(x)^2=0\)
   4.17.24 \(y(x)^2 \log (a y(x))-x y(x) y'(x)+y'(x)^2=0\)
   4.17.25 \(y'(x)^2-(2 x y(x)+1) y'(x)+2 x y(x)=0\)
   4.17.26 \(y'(x)^2-\left (y(x)^2+4\right ) y'(x)+y(x)^2+4=0\)
   4.17.27 \(-(x-y(x)) y(x) y'(x)+y'(x)^2-x y(x)^3=0\)
   4.17.28 \(x y(x)^2 y'(x)+y'(x)^2+y(x)^3=0\)
   4.17.29 \(-2 x^3 y(x)^2 y'(x)-4 x^2 y(x)^3+y'(x)^2=0\)
   4.17.30 \(x^4 y(x)^4-x \left (x^2+y(x)^2\right ) y(x) y'(x)+y'(x)^2=0\)
   4.17.31 \(2 x y(x)^3 y'(x)+y'(x)^2+y(x)^4=0\)
   4.17.32 \(y'(x)^2+2 y(x) \cot (x) y'(x)-y(x)^2=0\)
   4.17.33 \(y'(x)^2-3 x y(x)^{2/3} y'(x)+9 y(x)^{5/3}=0\)
   4.17.34 \(y'(x)^2=e^{4 x-2 y(x)} \left (y'(x)-1\right )\)
   4.17.35 \(2 y'(x)^2+x y'(x)-2 y(x)=0\)
   4.17.36 \(2 y'(x)^2-(1-x) y'(x)-y(x)=0\)
   4.17.37 \(-2 x^2 y'(x)+2 y'(x)^2+3 x y(x)=0\)
   4.17.38 \(2 y'(x)^2+2 (6 y(x)-1) y'(x)+3 y(x) (6 y(x)-1)=0\)
   4.17.39 \(3 y'(x)^2-2 x y'(x)+y(x)=0\)
   4.17.40 \(x^2+4 x y'(x)+3 y'(x)^2-y(x)=0\)
   4.17.41 \(4 y'(x)^2=9 x\)
   4.17.42 \(4 y'(x)^2+2 x e^{-2 y(x)} y'(x)-e^{-2 y(x)}=0\)
   4.17.43 \(4 y'(x)^2+2 e^{2 x-2 y(x)} y'(x)-e^{2 x-2 y(x)}=0\)
   4.17.44 \(5 y'(x)^2+3 x y'(x)-y(x)=0\)
   4.17.45 \(5 y'(x)^2+6 x y'(x)-2 y(x)=0\)
   4.17.46 \(3 x y(x)^4 y'(x)+9 y'(x)^2+y(x)^5=0\)
   4.17.47 \(x y'(x)^2=a\)
   4.17.48 \(x y'(x)^2=a-x^2\)
   4.17.49 \(x y'(x)^2=y(x)\)
   4.17.50 \(x y'(x)^2-2 y(x)+x=0\)