4.6 Problems 251 to 300

   4.6.1 \(3 x y'(x)=y(x) \left (3 x y(x)^3 \log (x)+1\right )\)
   4.6.2 \(x^2 y'(x)=a-y(x)\)
   4.6.3 \(x^2 y'(x)=a+b x+c x^2+x y(x)\)
   4.6.4 \(x^2 y'(x)=a+b x+c x^2-x y(x)\)
   4.6.5 \(x^2 y'(x)+(1-2 x) y(x)=x^2\)
   4.6.6 \(x^2 y'(x)=a+b x y(x)\)
   4.6.7 \(x^2 y'(x)=y(x) (a+b x)\)
   4.6.8 \(x^2 y'(x)+(x+2) x y(x)=\left (1-e^{-2 x}\right ) x-2\)
   4.6.9 \(x^2 y'(x)+2 (1-x) x y(x)=e^x \left (2 e^x-1\right )\)
   4.6.10 \(x^2 y'(x)+x^2+x y(x)+y(x)^2=0\)
   4.6.11 \(x^2 y'(x)=(-y(x)+2 x+1)^2\)
   4.6.12 \(x^2 y'(x)=a+b y(x)^2\)
   4.6.13 \(x^2 y'(x)=y(x) (a y(x)+x)\)
   4.6.14 \(x^2 y'(x)=y(x) (a x+b y(x))\)
   4.6.15 \(a x^2+b x y(x)+c y(x)^2+x^2 y'(x)=0\)
   4.6.16 \(x^2 y'(x)=a+b x^n+x^2 y(x)^2\)
   4.6.17 \(x^2 y'(x)+x y(x) (x y(x)+4)+2=0\)
   4.6.18 \(a x (1-x y(x))+x^2 y'(x)+x^2 \left (-y(x)^2\right )+2=0\)
   4.6.19 \(x^2 y'(x)=a+b x^2 y(x)^2\)
   4.6.20 \(x^2 y'(x)=a+b x^n+c x^2 y(x)^2\)
   4.6.21 \(x^2 y'(x)=a+b x y(x)+c x^2 y(x)^2\)
   4.6.22 \(x^2 y'(x)=a+b x y(x)+c x^4 y(x)^2\)
   4.6.23 \(x^2 y'(x)+y(x) \left (x^2+y(x)^2-x\right )=0\)
   4.6.24 \(x^2 y'(x)=2 y(x) \left (x-y(x)^2\right )\)
   4.6.25 \(x^2 y'(x)=a x^2 y(x)^2-a y(x)^3\)
   4.6.26 \(a y(x)^2+b x^2 y(x)^3+x^2 y'(x)=0\)
   4.6.27 \(x^2 y'(x)=y(x) \left (a x+b y(x)^3\right )\)
   4.6.28 \(x^2 y'(x)+x y(x)+\sqrt {y(x)}=0\)
   4.6.29 \(x^2 y'(x)=3 x \tan (y(x))+\sec (y(x))\)
   4.6.30 \(\left (1-x^2\right ) y'(x)=-x^2+y(x)+1\)
   4.6.31 \(\left (1-x^2\right ) y'(x)+1=x y(x)\)
   4.6.32 \(\left (1-x^2\right ) y'(x)=5-x y(x)\)
   4.6.33 \(a+\left (x^2+1\right ) y'(x)+x y(x)=0\)
   4.6.34 \(a+\left (x^2+1\right ) y'(x)-x y(x)=0\)
   4.6.35 \(a+\left (1-x^2\right ) y'(x)-x y(x)=0\)
   4.6.36 \(\left (1-x^2\right ) y'(x)+x y(x)-x=0\)
   4.6.37 \(\left (1-x^2\right ) y'(x)-x^2+x y(x)=0\)
   4.6.38 \(\left (1-x^2\right ) y'(x)+x^2+x y(x)=0\)
   4.6.39 \(\left (x^2+1\right ) y'(x)=x \left (x^2+1\right )-x y(x)\)
   4.6.40 \(\left (x^2+1\right ) y'(x)=x \left (3 x^2-y(x)\right )\)
   4.6.41 \(\left (1-x^2\right ) y'(x)+2 x y(x)=0\)
   4.6.42 \(\left (x^2+1\right ) y'(x)=2 x (x-y(x))\)
   4.6.43 \(\left (x^2+1\right ) y'(x)=2 x \left (x^2+1\right )^2+2 x y(x)\)
   4.6.44 \(\left (1-x^2\right ) y'(x)+\cos (x)=2 x y(x)\)
   4.6.45 \(\left (x^2+1\right ) y'(x)=\tan (x)-2 x y(x)\)
   4.6.46 \(\left (1-x^2\right ) y'(x)=a+4 x y(x)\)
   4.6.47 \(\left (x^2+1\right ) y'(x)=y(x) (a+2 b x)\)
   4.6.48 \(\left (x^2+1\right ) y'(x)=y(x)^2+1\)
   4.6.49 \(\left (1-x^2\right ) y'(x)=1-y(x)^2\)
   4.6.50 \(\left (1-x^2\right ) y'(x)=1-(2 x-y(x)) y(x)\)