4.11 Problems 501 to 550

   4.11.1 \((21 y(x)+9 x+3) y'(x)=-5 y(x)+7 x+45\)
   4.11.2 \(y'(x) (a x+b y(x))+x=0\)
   4.11.3 \(y'(x) (a x+b y(x))+y(x)=0\)
   4.11.4 \(y'(x) (a x+b y(x))+a y(x)+b x=0\)
   4.11.5 \(y'(x) (a x+b y(x))=a y(x)+b x\)
   4.11.6 \(\text {a1}+y'(x) (\text {a2}+b x+\text {c2} y(x))+b y(x)+\text {b1} x=0\)
   4.11.7 \(y'(x) (\text {a2}+\text {b2} y(x)+\text {c2} y(x))=\text {a1}+\text {b1} x+\text {c1} y(x)\)
   4.11.8 \(x y(x) y'(x)+y(x)^2+1=0\)
   4.11.9 \(x y(x) y'(x)=y(x)^2+x\)
   4.11.10 \(x^2+x y(x) y'(x)+y(x)^2=0\)
   4.11.11 \(x^4+x y(x) y'(x)-y(x)^2=0\)
   4.11.12 \(x y(x) y'(x)=a x^3 \cos (x)+y(x)^2\)
   4.11.13 \(x y(x) y'(x)=x^2-x y(x)+y(x)^2\)
   4.11.14 \(2 x^2+x y(x) y'(x)-2 x y(x)-y(x)^2=0\)
   4.11.15 \(x y(x) y'(x)=a+b y(x)^2\)
   4.11.16 \(x y(x) y'(x)=a x^n+b y(x)^2\)
   4.11.17 \(x y(x) y'(x)=\left (x^2+1\right ) \left (1-y(x)^2\right )\)
   4.11.18 \(x^2 \cot ^{-1}\left (\frac {y(x)}{x}\right )+x y(x) y'(x)-y(x)^2=0\)
   4.11.19 \(x^2 e^{-\frac {2 y(x)}{x}}+x y(x) y'(x)-y(x)^2=0\)
   4.11.20 \((x y(x)+1) y'(x)+y(x)^2=0\)
   4.11.21 \(x (y(x)+1) y'(x)-(1-x) y(x)=0\)
   4.11.22 \(x (1-y(x)) y'(x)+(x+1) y(x)=0\)
   4.11.23 \(x (1-y(x)) y'(x)+(1-x) y(x)=0\)
   4.11.24 \(a x+x (y(x)+2) y'(x)=0\)
   4.11.25 \((x (-y(x))+3 x+2) y'(x)+y(x)=0\)
   4.11.26 \(x (y(x)+4) y'(x)=y(x)^2+2 y(x)+2 x\)
   4.11.27 \(x (a+y(x)) y'(x)+b x+c y(x)=0\)
   4.11.28 \(x (a+y(x)) y'(x)=y(x) (A+B x)\)
   4.11.29 \(x (y(x)+x) y'(x)+y(x)^2=0\)
   4.11.30 \(x (x-y(x)) y'(x)+y(x)^2=0\)
   4.11.31 \(x (y(x)+x) y'(x)=x^2+y(x)^2\)
   4.11.32 \(2 x^2+x (x-y(x)) y'(x)+3 x y(x)-y(x)^2=0\)
   4.11.33 \(x \sqrt {x^2-y(x)^2}+x (y(x)+x) y'(x)-y(x) (y(x)+x)=0\)
   4.11.34 \((a+x (y(x)+x)) y'(x)=b y(x) (y(x)+x)\)
   4.11.35 \(x (y(x)+2 x) y'(x)=x^2+x y(x)-y(x)^2\)
   4.11.36 \(4 x^2+x (4 x-y(x)) y'(x)-6 x y(x)-y(x)^2=0\)
   4.11.37 \(x \left (x^3+y(x)\right ) y'(x)=\left (x^3-y(x)\right ) y(x)\)
   4.11.38 \(x \left (2 x^3+y(x)\right ) y'(x)=\left (2 x^3-y(x)\right ) y(x)\)
   4.11.39 \(x \left (2 x^3+y(x)\right ) y'(x)=6 y(x)^2\)
   4.11.40 \((1-x) y(x) y'(x)+x (1-y(x))=0\)
   4.11.41 \((a+x) (b+x) y'(x)=x y(x)\)
   4.11.42 \(-2 x^3+2 x y(x) y'(x)-y(x)^2+1=0\)
   4.11.43 \(a+2 x y(x) y'(x)+y(x)^2=0\)
   4.11.44 \(2 x y(x) y'(x)=a x+y(x)^2\)
   4.11.45 \(x^2+2 x y(x) y'(x)+y(x)^2=0\)
   4.11.46 \(2 x y(x) y'(x)=x^2+y(x)^2\)
   4.11.47 \(2 x y(x) y'(x)=4 (2 x+1) x^2+y(x)^2\)
   4.11.48 \(x^2 \left (a x^3+1\right )+2 x y(x) y'(x)=6 y(x)^2\)
   4.11.49 \(3 x^2+(2 x y(x)-x+3) y'(x)+y(x)^2-y(x)=0\)
   4.11.50 \(x (x-2 y(x)) y'(x)+y(x)^2=0\)