4.14 Problems 651 to 700

   4.14.1 \(x \left (a x y(x)+x^2+y(x)^2\right ) y'(x)=y(x) \left (b x y(x)+x^2+y(x)^2\right )\)
   4.14.2 \(x \left (x^2-2 y(x)^2\right ) y'(x)=y(x) \left (2 x^2-y(x)^2\right )\)
   4.14.3 \(x \left (x^2+2 y(x)^2\right ) y'(x)=y(x) \left (2 x^2+3 y(x)^2\right )\)
   4.14.4 \(2 x \left (5 x^2+y(x)^2\right ) y'(x)=x^2 y(x)-y(x)^3\)
   4.14.5 \(x \left (a x y(x)+x^2+2 y(x)^2\right ) y'(x)=y(x)^2 (a x+2 y(x))\)
   4.14.6 \(3 x y(x)^2 y'(x)=2 x-y(x)^3\)
   4.14.7 \(\left (3 x y(x)^2-4 x+1\right ) y'(x)=y(x) \left (2-y(x)^2\right )\)
   4.14.8 \(x \left (x-3 y(x)^2\right ) y'(x)+y(x) \left (2 x-y(x)^2\right )=0\)
   4.14.9 \(x^3+3 x \left (y(x)^2+x\right ) y'(x)-3 x y(x)-2 y(x)^3=0\)
   4.14.10 \(x \left (-3 x^3 y(x)+x^3+4 y(x)^2\right ) y'(x)=6 y(x)^3\)
   4.14.11 \(6 x y(x)^2 y'(x)+2 y(x)^3+x=0\)
   4.14.12 \(x \left (6 y(x)^2+x\right ) y'(x)-3 y(x)^3+x y(x)=0\)
   4.14.13 \(x \left (x^2-6 y(x)^2\right ) y'(x)=4 y(x) \left (x^2+3 y(x)^2\right )\)
   4.14.14 \(x \left (3 x-7 y(x)^2\right ) y'(x)+y(x) \left (5 x-3 y(x)^2\right )=0\)
   4.14.15 \(x^3+x^2 y(x)^2 y'(x)-x+1=0\)
   4.14.16 \(\left (1-x^2 y(x)^2\right ) y'(x)=x y(x)^3\)
   4.14.17 \(\left (1-x^2 y(x)^2\right ) y'(x)=y(x)^2 (x y(x)+1)\)
   4.14.18 \(x \left (x y(x)^2+1\right ) y'(x)+y(x)=0\)
   4.14.19 \(x \left (x y(x)^2+1\right ) y'(x)=y(x) \left (2-3 x y(x)^2\right )\)
   4.14.20 \(x^2 (a+y(x))^2 y'(x)=\left (x^2+1\right ) \left (a^2+y(x)^2\right )\)
   4.14.21 \(\left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) \left (1-y(x)^2\right )=0\)
   4.14.22 \(\left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) (1-y(x))^2=0\)
   4.14.23 \(\left (-x^3+6 x^2 y(x)^2+1\right ) y'(x)=x \left (-4 y(x)^3+3 x y(x)+6\right )\)
   4.14.24 \(x \left (4 x^2 y(x)-12 x y(x)^2+5 x+3\right ) y'(x)+y(x) \left (6 x^2 y(x)-8 x y(x)^2+10 x+3\right )=0\)
   4.14.25 \(x^3 \left (y(x)^2+1\right ) y'(x)+3 x^2 y(x)=0\)
   4.14.26 \(y(x) \left (x^2 y(x)^2+1\right )+x (1-x y(x))^2 y'(x)=0\)
   4.14.27 \(\left (1-x^4 y(x)^2\right ) y'(x)=x^3 y(x)^3\)
   4.14.28 \(\left (3 x-y(x)^3\right ) y'(x)=x^2-3 y(x)\)
   4.14.29 \(\left (x^3-y(x)^3\right ) y'(x)+x^2 y(x)=0\)
   4.14.30 \(x^2 (a x+3 y(x))+\left (x^3+y(x)^3\right ) y'(x)=0\)
   4.14.31 \(\left (-x^2 y(x)-y(x)^3+x\right ) y'(x)=x^3+x y(x)^2-y(x)\)
   4.14.32 \(\left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)+x \left (x^2-y(x)^2\right )=a^2 y(x)\)
   4.14.33 \(y(x) \left (a+x^2+y(x)^2\right ) y'(x)=x \left (a-x^2-y(x)^2\right )\)
   4.14.34 \(y(x) \left (3 x^2+y(x)^2\right ) y'(x)+x \left (x^2+3 y(x)^2\right )=0\)
   4.14.35 \(y(x) \left (a-3 x^2-y(x)^2\right ) y'(x)+x \left (a-x^2+y(x)^2\right )=0\)
   4.14.36 \(2 y(x)^3 y'(x)=x^3-x y(x)^2\)
   4.14.37 \(y(x) \left (2 y(x)^2+1\right ) y'(x)=x \left (2 x^2+1\right )\)
   4.14.38 \(x^3+y(x) \left (3 x^2+2 y(x)^2\right ) y'(x)=0\)
   4.14.39 \(y(x) \left (5 x^2+2 y(x)^2\right ) y'(x)+x \left (x^2+5 y(x)^2\right )=0\)
   4.14.40 \(2 x^3+3 x^2 y(x)+\left (-x^3+x^2+3 x y(x)^2+2 y(x)^3\right ) y'(x)-y(x)^3+y(x)^2=0\)
   4.14.41 \(4 x^3+9 x^2 y(x)+\left (3 x^3+6 x^2 y(x)-3 x y(x)^2+20 y(x)^3\right ) y'(x)+6 x y(x)^2-y(x)^3=0\)
   4.14.42 \(\left (a y(x)^3+x^3\right ) y'(x)=x^2 y(x)\)
   4.14.43 \(y'(x) \left (a x^2-b x^3+3 c x y(x)^2+2 c y(x)^3\right )+a y(x)^2+2 b x^3+3 b x^2 y(x)-c y(x)^3=0\)
   4.14.44 \(x y(x)^3 y'(x)=\left (1-x^2\right ) \left (y(x)^2+1\right )\)
   4.14.45 \(x \left (x-y(x)^3\right ) y'(x)=y(x) \left (y(x)^3+3 x\right )\)
   4.14.46 \(x \left (2 x^3+y(x)^3\right ) y'(x)=y(x) \left (2 x^3-x^2 y(x)+y(x)^3\right )\)
   4.14.47 \(x \left (2 x^3-y(x)^3\right ) y'(x)=y(x) \left (x^3-2 y(x)^3\right )\)
   4.14.48 \(x \left (x^3+3 x^2 y(x)+y(x)^3\right ) y'(x)=y(x)^2 \left (3 x^2+y(x)^2\right )\)
   4.14.49 \(x \left (x^3-2 y(x)^3\right ) y'(x)=y(x) \left (2 x^3-y(x)^3\right )\)
   4.14.50 \(x \left (x^4-2 y(x)^3\right ) y'(x)+y(x) \left (2 x^4+y(x)^3\right )=0\)