4.4 Problems 151 to 200

   4.4.1 \(x y'(x)=x \sin (x)-y(x)\)
   4.4.2 \(x y'(x)=x^2 \sin (x)+y(x)\)
   4.4.3 \(x y'(x)=x^n \log (x)-y(x)\)
   4.4.4 \(x y'(x)=\sin (x)-2 y(x)\)
   4.4.5 \(x y'(x)=a y(x)\)
   4.4.6 \(x y'(x)=a y(x)+x+1\)
   4.4.7 \(x y'(x)=a x+b y(x)\)
   4.4.8 \(x y'(x)=a x^2+b y(x)\)
   4.4.9 \(x y'(x)=a+b x^n+c y(x)\)
   4.4.10 \(x y'(x)+(3-x) y(x)+2=0\)
   4.4.11 \((a x+2) y(x)+x y'(x)+x=0\)
   4.4.12 \(y(x) (a+b x)+x y'(x)=0\)
   4.4.13 \(x y'(x)=x^3+\left (1-2 x^2\right ) y(x)\)
   4.4.14 \(x y'(x)=a x-\left (1-b x^2\right ) y(x)\)
   4.4.15 \(\left (2-a x^2\right ) y(x)+x y'(x)+x=0\)
   4.4.16 \(x^2+x y'(x)+y(x)^2=0\)
   4.4.17 \(x y'(x)=x^2+y(x) (y(x)+1)\)
   4.4.18 \(x y'(x)+y(x)^2-y(x)=x^{2/3}\)
   4.4.19 \(x y'(x)=a+b y(x)^2\)
   4.4.20 \(x y'(x)=a x^2+b y(x)^2+y(x)\)
   4.4.21 \(x y'(x)=a x^{2 n}+y(x) (b y(x)+n)\)
   4.4.22 \(x y'(x)=a x^n+b y(x)+c y(x)^2\)
   4.4.23 \(x y'(x)=a x^n+b y(x)+c y(x)^2+k\)
   4.4.24 \(a+x y'(x)+x y(x)^2=0\)
   4.4.25 \(x y'(x)+y(x) (1-x y(x))=0\)
   4.4.26 \(x y'(x)=y(x) (1-x y(x))\)
   4.4.27 \(x y'(x)=y(x) (x y(x)+1)\)
   4.4.28 \(x y'(x)=a x^3 y(x) (1-x y(x))\)
   4.4.29 \(x y'(x)=x^3+\left (2 x^2+1\right ) y(x)+x y(x)^2\)
   4.4.30 \(x y'(x)=y(x) (2 x y(x)+1)\)
   4.4.31 \(y(x) (a x y(x)+2)+b x+x y'(x)=0\)
   4.4.32 \(\text {a0}+\text {a1} x+y(x) (\text {a2}+\text {a3} x y(x))+x y'(x)=0\)
   4.4.33 \(a x^2 y(x)^2+x y'(x)+2 y(x)=b\)
   4.4.34 \(\frac {1}{2} (n-m) y(x)+x^m+x^n y(x)^2+x y'(x)=0\)
   4.4.35 \(y(x) \left (a+b x^n y(x)\right )+x y'(x)=0\)
   4.4.36 \(x y'(x)=a x^m-b y(x)-c x^n y(x)^2\)
   4.4.37 \(x y'(x)=a x^n (x-y(x))^2-y(x)+2 x\)
   4.4.38 \(y(x) (1-a y(x) \log (x))+x y'(x)=0\)
   4.4.39 \(x y'(x)=f(x) \left (x^2-y(x)^2\right )+y(x)\)
   4.4.40 \(x y'(x)=y(x) \left (y(x)^2+1\right )\)
   4.4.41 \(x y'(x)+y(x) \left (1-x y(x)^2\right )=0\)
   4.4.42 \(x y'(x)+y(x)=a \left (x^2+1\right ) y(x)^3\)
   4.4.43 \(x y'(x)=a y(x)+b \left (x^2+1\right ) y(x)^3\)
   4.4.44 \(x y'(x)+2 y(x)=a x^{2 k} y(x)^k\)
   4.4.45 \(x y'(x)=4 \left (y(x)-\sqrt {y(x)}\right )\)
   4.4.46 \(x y'(x)+2 y(x)=\sqrt {y(x)^2+1}\)
   4.4.47 \(x y'(x)=\sqrt {x^2+y(x)^2}+y(x)\)
   4.4.48 \(x y'(x)=\sqrt {x^2-y(x)^2}+y(x)\)
   4.4.49 \(x y'(x)=x \sqrt {x^2+y(x)^2}+y(x)\)
   4.4.50 \(x y'(x)=y(x)-x (x-y(x)) \sqrt {x^2+y(x)^2}\)