4.21 Problems 1001 to 1050

   4.21.1 \(a^2 \left (-x^2\right )-3 a^2 x y(x) y'(x)+\left (1-a^2\right ) y(x)^2 y'(x)^2+y(x)^2=0\)
   4.21.2 \((a-b) y(x)^2 y'(x)^2-a b+a y(x)^2-b x^2-2 b x y(x) y'(x)=0\)
   4.21.3 \(a^2 y'(x)^2 \left (b^2-(c x-a y(x))^2\right )+c^2 \left (b^2-(c x-a y(x))^2\right )+2 a b^2 c y'(x)=0\)
   4.21.4 \(a^2 x+y(x)^3 \left (-y'(x)\right )+x y(x)^2 y'(x)^2=0\)
   4.21.5 \(\left (a-x^3-y(x)^3\right ) y'(x)+x^2 y(x)+x y(x)^2 y'(x)^2=0\)
   4.21.6 \(-x \left (x^2-2 y(x)^2\right )-2 y(x)^3 y'(x)+x y(x)^2 y'(x)^2=0\)
   4.21.7 \(-a+y(x)^3 \left (-y'(x)\right )+2 x y(x)^2 y'(x)^2=0\)
   4.21.8 \(4 x^2 y(x)^2 y'(x)^2=\left (x^2+y(x)^2\right )^2\)
   4.21.9 \(-2 x \left (x^3+2 y(x)^2\right ) y(x) y'(x)+\left (2 x^3+y(x)^2\right ) y(x)^2+4 x^2 y(x)^2 y'(x)^2=0\)
   4.21.10 \(4 y(x)^3 y'(x)^2-4 x y'(x)+y(x)=0\)
   4.21.11 \(x y(x) \left (x^2+y(x)^2\right ) y'(x)^2-x y(x) \left (x^2+y(x)^2\right )-\left (x^4+x^2 y(x)^2+y(x)^4\right ) y'(x)=0\)
   4.21.12 \(x \left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)^2+\left (2 a^2 x y(x)+\left (x^2-y(x)^2\right )^2\right ) y'(x)+a^2 y(x)^2-x \left (x^2-y(x)^2\right ) y(x)=0\)
   4.21.13 \(x \left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)^2-\left (2 a^2 x y(x)-\left (x^2-y(x)^2\right )^2\right ) y'(x)+a^2 y(x)^2-x \left (x^2-y(x)^2\right ) y(x)=0\)
   4.21.14 \(\left (x^2-y(x)^2 \left (x^2+y(x)^2\right )\right ) y'(x)^2-2 x y(x) y'(x)+y(x)^2=0\)
   4.21.15 \(-2 x \left (x^2+2 y(x)^2\right ) y(x) y'(x)+\left (x^4+y(x)^2 \left (x^2-y(x)^2\right )\right ) y'(x)^2+y(x)^4=0\)
   4.21.16 \(y(x)^5 \left (-y'(x)\right )+3 x y(x)^4 y'(x)^2+1=0\)
   4.21.17 \(-a-3 y(x)^5 y'(x)+9 x y(x)^4 y'(x)^2=0\)
   4.21.18 \(9 \left (1-x^2\right ) y(x)^4 y'(x)^2+4 x^2+6 x y(x)^5 y'(x)=0\)
   4.21.19 \(y'(x)^2 \left (a^2 r(x,y(x))-x^2\right )+a^2 r(x,y(x))+2 x y(x) y'(x)-y(x)^2=0\)
   4.21.20 \(y'(x)^2 \left (a r(x,y(x))-x^2\right )+a r(x,y(x))+2 x y(x) y'(x)-y(x)^2=0\)
   4.21.21 \(y'(x)^3=a+b x\)
   4.21.22 \(y'(x)^3=a x^n\)
   4.21.23 \(y'(x)^3-y(x)+x=0\)
   4.21.24 \(y'(x)^3=f(x) \left (a+b y(x)+c y(x)^2\right )\)
   4.21.25 \(y'(x)^3=(y(x)-a)^2 (y(x)-b)^2\)
   4.21.26 \(f(x) (y(x)-a)^2 (y(x)-b)^2+y'(x)^3=0\)
   4.21.27 \(f(x) (y(x)-a)^2 (y(x)-b)^2 (y(x)-c)^2+y'(x)^3=0\)
   4.21.28 \(a-b x+y'(x)^3+y'(x)=0\)
   4.21.29 \(y'(x)^3+y'(x)-y(x)=0\)
   4.21.30 \(y'(x)^3+y'(x)=e^{y(x)}\)
   4.21.31 \(y'(x)^3-7 y'(x)+6=0\)
   4.21.32 \(a y(x)+y'(x)^3-x y'(x)=0\)
   4.21.33 \(y'(x)^3+2 x y'(x)-y(x)=0\)
   4.21.34 \(y'(x)^3-2 x y'(x)-y(x)=0\)
   4.21.35 \(-a x y'(x)+x^3+y'(x)^3=0\)
   4.21.36 \(a x y'(x)-a y(x)+y'(x)^3=0\)
   4.21.37 \(-(a+b x) y'(x)+b y(x)+y'(x)^3=0\)
   4.21.38 \(y'(x)^3-y(x) y'(x)-x=0\)
   4.21.39 \(y'(x)^3-(y(x)+3) y'(x)+x=0\)
   4.21.40 \(y'(x)^3-2 y(x) y'(x)+y(x)^2=0\)
   4.21.41 \(-a x y(x) y'(x)+2 a y(x)^2+y'(x)^3=0\)
   4.21.42 \(-\left (x^3+x y(x)+y(x)^2\right ) y'(x)+y'(x)^3+x y(x) (y(x)+x)=0\)
   4.21.43 \(-x y(x)^4 y'(x)+y'(x)^3-y(x)^5=0\)
   4.21.44 \(y'(x)^3+e^{3 x-2 y(x)} \left (y'(x)-1\right )=0\)
   4.21.45 \(y'(x)^3+\left (e^{2 x}+e^{3 x}\right ) e^{-2 y(x)} y'(x)-e^{3 x-2 y(x)}=0\)
   4.21.46 \(y'(x)^3+y'(x)^2-y(x)=0\)
   4.21.47 \(y'(x)^3-y'(x)^2+y(x)^2=0\)
   4.21.48 \(y'(x)^3-y'(x)^2+x y'(x)-y(x)=0\)
   4.21.49 \(a b x-a y'(x)^2+b y(x)+y'(x)^3=0\)
   4.21.50 \(\text {a0} y'(x)^2+\text {a1} y'(x)+\text {a2}+\text {a3} y(x)+y'(x)^3=0\)