4.7 Problems 301 to 350

   4.7.1 \(\left (1-x^2\right ) y'(x)=n \left (y(x)^2-2 x y(x)+1\right )\)
   4.7.2 \(\left (x^2+1\right ) y'(x)+x (1-y(x)) y(x)=0\)
   4.7.3 \(\left (1-x^2\right ) y'(x)=x y(x) (a y(x)+1)\)
   4.7.4 \(\left (x^2+1\right ) y'(x)=y(x)^2-2 x \left (y(x)^2+1\right ) y(x)+1\)
   4.7.5 \(\left (x^2+1\right ) y'(x)+x \sin (y(x)) \cos (y(x))=x \left (x^2+1\right ) \cos ^2(y(x))\)
   4.7.6 \(\left (x^2+1\right ) y'(x)=x^2-y(x) \cot ^{-1}(x)+1\)
   4.7.7 \(\left (4-x^2\right ) y'(x)+4 y(x)=(x+2) y(x)^2\)
   4.7.8 \(\left (a^2+x^2\right ) y'(x)=b+x y(x)\)
   4.7.9 \(\left (a^2+x^2\right ) y'(x)=\left (\sqrt {a^2+x^2}+x\right ) (b+y(x))\)
   4.7.10 \(\left (a^2+x^2\right ) y'(x)+(x-y(x)) y(x)=0\)
   4.7.11 \(\left (a^2+x^2\right ) y'(x)=a^2-2 y(x)^2+3 x y(x)\)
   4.7.12 \(\left (a^2+x^2\right ) y'(x)+b x y(x)^2+x y(x)=0\)
   4.7.13 \((1-x) x y'(x)=a+(x+1) y(x)\)
   4.7.14 \((1-x) x y'(x)=2 (x y(x)+1)\)
   4.7.15 \((1-x) x y'(x)=2 (x y(x)-1)\)
   4.7.16 \(x (x+1) y'(x)=(1-2 x) y(x)\)
   4.7.17 \((1-x) x y'(x)+(2 x+1) y(x)=a\)
   4.7.18 \((1-x) x y'(x)=a+2 (2-x) y(x)\)
   4.7.19 \((1-x) x y'(x)-3 x y(x)+y(x)+2=0\)
   4.7.20 \(x (x+1) y'(x)=\left (x^2+x-1\right ) y(x)+(x+1) \left (x^2-1\right )\)
   4.7.21 \(x^2+(x-3) (x-2) y'(x)+3 x y(x)-8 y(x)=0\)
   4.7.22 \(x (a+x) y'(x)=y(x) (b+c y(x))\)
   4.7.23 \((a+x)^2 y'(x)=2 (a+x) (b+y(x))\)
   4.7.24 \(k (-a+y(x)+x)^2+(x-a)^2 y'(x)+y(x)^2=0\)
   4.7.25 \((x-a) (x-b) y'(x)+k y(x)=0\)
   4.7.26 \((x-a) (x-b) y'(x)=y(x) (-a-b+2 x)+(x-a) (x-b)\)
   4.7.27 \((x-a) (x-b) y'(x)=c y(x)^2\)
   4.7.28 \(k (y(x)-a) (y(x)-b)+(x-a) (x-b) y'(x)=0\)
   4.7.29 \(k (-a+y(x)+x) (-b+y(x)+x)+(x-a) (x-b) y'(x)+y(x)^2=0\)
   4.7.30 \(2 x^2 y'(x)=y(x)\)
   4.7.31 \(2 x^2 y'(x)+2 x^2 y(x) \cot (x)+x \cot (x)-1=0\)
   4.7.32 \(2 x^2 y'(x)+x^2 \left (-y(x)^2\right )+2 x y(x)+1=0\)
   4.7.33 \(2 x^2 y'(x)=\left (x^2-y(x)^2\right ) (1-x \cot (x))+2 x y(x)\)
   4.7.34 \(2 \left (1-x^2\right ) y'(x)=\sqrt {1-x^2}+(x+1) y(x)\)
   4.7.35 \((1-2 x) x y'(x)+(1-4 x) y(x)+1=0\)
   4.7.36 \((1-2 x) x y'(x)=y(x)^2-(4 x+1) y(x)+4 x\)
   4.7.37 \(2 (1-x) x y'(x)+(1-2 x) y(x)+x=0\)
   4.7.38 \(2 (1-x) x y'(x)+(1-x) y(x)^2+x=0\)
   4.7.39 \(2 \left (x^2+x+1\right ) y'(x)=8 x^2-(2 x+1) y(x)+1\)
   4.7.40 \(4 \left (x^2+1\right ) y'(x)-x^2-4 x y(x)=0\)
   4.7.41 \(a x^2 y'(x)=a x y(x)+b^2 y(x)^2+x^2\)
   4.7.42 \(\left (a+b x^2\right ) y'(x)=A+B y(x)^2\)
   4.7.43 \(\left (a+b x^2\right ) y'(x)=c x y(x) \log (y(x))\)
   4.7.44 \(x (a x+1) y'(x)+a-y(x)=0\)
   4.7.45 \((a+b x)^2 y'(x)+y(x)^3 (a+b x)+c y(x)^2=0\)
   4.7.46 \(x^3 y'(x)=a+b x^2 y(x)\)
   4.7.47 \(x^3 y'(x)=x^2 y(x)-x^2+3\)
   4.7.48 \(x^3 y'(x)=x^4+y(x)^2\)
   4.7.49 \(x^3 y'(x)=y(x) \left (x^2+y(x)\right )\)
   4.7.50 \(x^3 y'(x)=x^2 (y(x)-1)+y(x)^2\)