4.22 Problems 1051 to 1100

   4.22.1 \(y'(x)^3+x y'(x)^2-y(x)=0\)
   4.22.2 \(-x^3-(1-3 x) x y'(x)+y'(x)^3+(1-3 x) y'(x)^2-1=0\)
   4.22.3 \(y'(x)^3-y(x) y'(x)^2+y(x)^2=0\)
   4.22.4 \(y'(x)^3+y'(x)^2 (\cos (x) \cot (x)-y(x))-y'(x) (y(x) \cos (x) \cot (x)+1)+y(x)=0\)
   4.22.5 \(y'(x)^3+\left (2 x-y(x)^2\right ) y'(x)^2-2 x y(x)^2 y'(x)=0\)
   4.22.6 \(\left (x^2+2 x y(x)^2-y(x)^2\right ) y'(x)-y(x)^2 \left (x^2-y(x)^2\right )+y'(x)^3-\left (y(x)^2+2 x\right ) y'(x)^2=0\)
   4.22.7 \(-x^3 y(x)^3+x \left (x^2+x y(x)+y(x)^2\right ) y(x) y'(x)-\left (x^2+x y(x)+y(x)^2\right ) y'(x)^2+y'(x)^3=0\)
   4.22.8 \(-x^3 y(x)^6+x \left (x^2+y(x)^4+x y(x)^2\right ) y(x)^2 y'(x)-\left (x^2+y(x)^4+x y(x)^2\right ) y'(x)^2+y'(x)^3=0\)
   4.22.9 \(2 y'(x)^3+x y'(x)-2 y(x)=0\)
   4.22.10 \(2 y'(x)^3+y'(x)^2-y(x)=0\)
   4.22.11 \(x^4 \left (-y'(x)\right )+2 x^3 y(x)+3 y'(x)^3=0\)
   4.22.12 \(4 y'(x)^3+4 y'(x)=x\)
   4.22.13 \(8 y'(x)^3+12 y'(x)^2=27 (y(x)+x)\)
   4.22.14 \(a+x y'(x)^3-y(x) y'(x)^2=0\)
   4.22.15 \(x y'(x)^3+(2 x-y(x)) y'(x)^2+(2-2 y(x)) y'(x)-y(x)+1=0\)
   4.22.16 \(-\left (x^2+y(x)+x\right ) y'(x)^2+\left (x^2+x y(x)+y(x)\right ) y'(x)+x y'(x)^3-x y(x)=0\)
   4.22.17 \(4 x^2+x y'(x)^3-2 y(x) y'(x)^2=0\)
   4.22.18 \(2 x y'(x)^3-3 y(x) y'(x)^2-x=0\)
   4.22.19 \(4 x y'(x)^3-6 y(x) y'(x)^2+3 y(x)-x=0\)
   4.22.20 \(8 x y'(x)^3-12 y(x) y'(x)^2+9 y(x)=0\)
   4.22.21 \(x^2 y'(x)^3-2 x y(x) y'(x)^2+y(x)^2 y'(x)+1=0\)
   4.22.22 \(b x \left (a^2-x^2\right ) y'(x)^2+\left (a^2-x^2\right ) y'(x)^3-b x-y'(x)=0\)
   4.22.23 \(x \left (x^5+3 y(x)^2\right ) y'(x)-2 x^5 y(x)-3 x^2 y(x) y'(x)^2+x y'(x)^3-y(x)^3=0\)
   4.22.24 \(2 x^3 y'(x)^3+6 x^2 y(x) y'(x)^2-(1-6 x y(x)) y(x) y'(x)+2 y(x)^3=0\)
   4.22.25 \(8 x^3 y'(x)^3+12 x^2 y(x) y'(x)^2-\left (1-6 x y(x)^2\right ) y'(x)+y(x)^3=0\)
   4.22.26 \(x^4 y'(x)^3-x^3 y(x) y'(x)^2-x^2 y(x)^2 y'(x)+x y(x)^3=1\)
   4.22.27 \(x^6 y'(x)^3-x y'(x)-y(x)=0\)
   4.22.28 \(y(x) y'(x)^3-3 x y'(x)+3 y(x)=0\)
   4.22.29 \(2 y(x) y'(x)^3-3 x y'(x)+2 y(x)=0\)
   4.22.30 \(2 y(x) y'(x)^3+3 y(x) y'(x)+x=0\)
   4.22.31 \(2 y(x) y'(x)^3-y(x) y'(x)^2+2 x y'(x)-x=0\)
   4.22.32 \((2 y(x)+x) y'(x)^3+3 (y(x)+x) y'(x)^2+(y(x)+2 x) y'(x)=0\)
   4.22.33 \(y(x)^2 y'(x)^3-x y'(x)+y(x)=0\)
   4.22.34 \(y(x)^2 y'(x)^3+2 x y'(x)-y(x)=0\)
   4.22.35 \(4 y(x)^2 y'(x)^3-2 x y'(x)+y(x)=0\)
   4.22.36 \(16 y(x)^2 y'(x)^3+2 x y'(x)-y(x)=0\)
   4.22.37 \(x \left (x^2+1\right ) y'(x)-x^2 y(x)+y(x)^3 \left (-y'(x)^2\right )+x y(x)^2 y'(x)^3=0\)
   4.22.38 \(x^7 y(x)^2 y'(x)^3+\left (1-3 x^6 y(x)^3\right ) y'(x)^2+3 x^5 y(x)^4 y'(x)-x^4 y(x)^5=0\)
   4.22.39 \(y(x)^3 y'(x)^3-x y'(x)+y(x)=0\)
   4.22.40 \(x^3+3 x^2 y(x) y'(x)+y(x)^3 y'(x)^3-(1-3 x) y(x)^2 y'(x)^2-y(x)^2=0\)
   4.22.41 \(y(x)^4 y'(x)^3-6 x y'(x)+2 y(x)=0\)
   4.22.42 \(y'(x)^4=(y(x)-a)^3 (y(x)-b)^2\)
   4.22.43 \(f(x) (y(x)-a)^3 (y(x)-b)^2+y'(x)^4=0\)
   4.22.44 \(f(x) (y(x)-a)^3 (y(x)-b)^3+y'(x)^4=0\)
   4.22.45 \(f(x) (y(x)-a)^3 (y(x)-b)^3 (y(x)-c)^2+y'(x)^4=0\)
   4.22.46 \(y'(x)^4+x y'(x)-3 y(x)=0\)
   4.22.47 \(y'(x)^4-3 (1-x) y'(x)^2+3 (1-2 y(x)) y'(x)+3 x=0\)
   4.22.48 \(-4 x^2 y(x) y'(x)^2+y'(x)^4+16 x y(x)^2 y'(x)-16 y(x)^3=0\)
   4.22.49 \(y'(x)^4+4 y(x) y'(x)^3+6 y(x)^2 y'(x)^2-\left (1-4 y(x)^3\right ) y'(x)-y(x) \left (3-y(x)^3\right )=0\)
   4.22.50 \(2 y'(x)^4-y(x) y'(x)-2=0\)