4.13 Problems 601 to 650

   4.13.1 \(\left (x^2+y(x)^2\right ) y'(x)+x y(x)=0\)
   4.13.2 \(\left (x^2+y(x)^2\right ) y'(x)=x y(x)\)
   4.13.3 \(\left (x^2-y(x)^2\right ) y'(x)=2 x y(x)\)
   4.13.4 \(\left (x^2-y(x)^2\right ) y'(x)+x (2 y(x)+x)=0\)
   4.13.5 \(\left (x^2+y(x)^2\right ) y'(x)+2 x (y(x)+2 x)=0\)
   4.13.6 \(\left (-x^2+y(x)^2+1\right ) y'(x)=x^2-y(x)^2+1\)
   4.13.7 \(\left (a^2+x^2+y(x)^2\right ) y'(x)+2 x y(x)=0\)
   4.13.8 \(\left (a^2+x^2+y(x)^2\right ) y'(x)+b^2+x^2+2 x y(x)=0\)
   4.13.9 \(\left (x^2+y(x)^2+x\right ) y'(x)=y(x)\)
   4.13.10 \(\left (3 x^2-y(x)^2\right ) y'(x)=2 x y(x)\)
   4.13.11 \(\left (x^4+y(x)^2\right ) y'(x)=4 x^3 y(x)\)
   4.13.12 \(y(x) (y(x)+1) y'(x)=x (x+1)\)
   4.13.13 \(\left (y(x)^2+2 y(x)+x\right ) y'(x)+y(x)^2 (y(x)+x)^2+y(x) (y(x)+1)=0\)
   4.13.14 \(\left (x^2+y(x)^2+2 y(x)\right ) y'(x)+2 x=0\)
   4.13.15 \(\left (x^3-y(x)^2+2 y(x)\right ) y'(x)+3 x^2 y(x)=0\)
   4.13.16 \(\left (y(x)^2+x y(x)+y(x)+1\right ) y'(x)+y(x)+1=0\)
   4.13.17 \((y(x)+x)^2 y'(x)=a^2\)
   4.13.18 \((x-y(x))^2 y'(x)=a^2\)
   4.13.19 \(\left (x^2+2 x y(x)-y(x)^2\right ) y'(x)+x^2-2 x y(x)+y(x)^2=0\)
   4.13.20 \((x-y(x))^2 y'(x)=(-y(x)+x+1)^2\)
   4.13.21 \((y(x)+x)^2 y'(x)=(y(x)+x+2)^2\)
   4.13.22 \((y(x)+x)^2 y'(x)=x^2-2 x y(x)+5 y(x)^2\)
   4.13.23 \(y'(x) (a+b+y(x)+x)^2=2 (a+y(x))^2\)
   4.13.24 \(\left (2 x^2+4 x y(x)-y(x)^2\right ) y'(x)=x^2-4 x y(x)-2 y(x)^2\)
   4.13.25 \((y(x)+3 x)^2 y'(x)=4 y(x) (2 y(x)+3 x)\)
   4.13.26 \((-y(x)-3 x+1)^2 y'(x)=(-4 y(x)-6 x+3) (1-2 y(x))\)
   4.13.27 \(y'(x) \left (\cot (x)-2 y(x)^2\right )=y(x)^3 \csc (x) \sec (x)\)
   4.13.28 \(3 y(x)^2 y'(x)=a y(x)^3+x+1\)
   4.13.29 \(\left (x^2-3 y(x)^2\right ) y'(x)+2 x y(x)+1=0\)
   4.13.30 \(\left (2 x^2+3 y(x)^2\right ) y'(x)+x (y(x)+3 x)=0\)
   4.13.31 \(3 \left (x^2-y(x)^2\right ) y'(x)-2 y(x)^3+6 x (x+1) y(x)+3 e^x=0\)
   4.13.32 \(\left (3 x^2+2 x y(x)+4 y(x)^2\right ) y'(x)+2 x^2+6 x y(x)+y(x)^2=0\)
   4.13.33 \((2 y(x)-3 x+1)^2 y'(x)=(-3 y(x)+2 x+4)^2\)
   4.13.34 \(\left (-3 x^2 y(x)+6 y(x)^2+1\right ) y'(x)+x^2-3 x y(x)^2=0\)
   4.13.35 \(a+(x-6 y(x))^2 y'(x)-6 y(x)^2+2 x y(x)=0\)
   4.13.36 \(\left (a y(x)^2+x^2\right ) y'(x)=x y(x)\)
   4.13.37 \(\left (a y(x)^2+x^2+x y(x)\right ) y'(x)=a x^2+x y(x)+y(x)^2\)
   4.13.38 \(\left (a x^2-a y(x)^2+2 x y(x)\right ) y'(x)-2 a x y(x)+x^2-y(x)^2=0\)
   4.13.39 \(y'(x) \left (x^2 (a+2 b)+2 x (2 b+c) y(x)+3 c y(x)^2\right )+2 x (a+2 b) y(x)+3 a x^2+(2 b+c) y(x)^2=0\)
   4.13.40 \(y'(x) \left (a x^2+2 b x y(x)+c y(x)^2\right )+2 a x y(x)+b y(x)^2+k x^2=0\)
   4.13.41 \(x \left (1-y(x)^2\right ) y'(x)=\left (x^2+1\right ) y(x)\)
   4.13.42 \(x \left (3 x-y(x)^2\right ) y'(x)+y(x) \left (5 x-2 y(x)^2\right )=0\)
   4.13.43 \(x \left (x^2+y(x)^2\right ) y'(x)=y(x) \left (x^4+x^2+y(x)^2\right )\)
   4.13.44 \(x \left (-x^2+y(x)^2+1\right ) y'(x)+y(x) \left (x^2-y(x)^2+1\right )=0\)
   4.13.45 \(x \left (a-x^2-y(x)^2\right ) y'(x)+y(x) \left (a+x^2+y(x)^2\right )=0\)
   4.13.46 \(x \left (2 x^2+y(x)^2\right ) y'(x)=y(x) \left (2 x^2+3 y(x)^2\right )\)
   4.13.47 \(\left (x \left (a-x^2-y(x)^2\right )+y(x)\right ) y'(x)-y(x) \left (a-x^2-y(x)^2\right )+x=0\)
   4.13.48 \(x (a+y(x))^2 y'(x)=b y(x)^2\)
   4.13.49 \(x \left (x^2-x y(x)+y(x)^2\right ) y'(x)+y(x) \left (x^2+x y(x)+y(x)^2\right )=0\)
   4.13.50 \(x \left (x^2-x y(x)-y(x)^2\right ) y'(x)=y(x) \left (x^2+x y(x)-y(x)^2\right )\)