4.5 Problems 201 to 250

   4.5.1 \(x y'(x)=a \sqrt {b^2 x^2+y(x)^2}+y(x)\)
   4.5.2 \(\cos (y(x)) \left (\sin (y(x))-3 x^2 \cos (y(x))\right )+x y'(x)=0\)
   4.5.3 \(x y'(x)-y(x)+x \cos \left (\frac {y(x)}{x}\right )+x=0\)
   4.5.4 \(x y'(x)=y(x)-x \cos ^2\left (\frac {y(x)}{x}\right )\)
   4.5.5 \(x y'(x)=\left (1-2 x^2\right ) \cot ^2(y(x))\)
   4.5.6 \(x y'(x)=y(x)-\cot ^2(y(x))\)
   4.5.7 \(x y'(x)+y(x)+2 x \sec (x y(x))=0\)
   4.5.8 \(x y'(x)-y(x)+x \sec \left (\frac {y(x)}{x}\right )=0\)
   4.5.9 \(x y'(x)=y(x)+x \sec ^2\left (\frac {y(x)}{x}\right )\)
   4.5.10 \(x y'(x)=\sin (x-y(x))\)
   4.5.11 \(x y'(x)=y(x)+x \sin \left (\frac {y(x)}{x}\right )\)
   4.5.12 \(x y'(x)+\tan (y(x))=0\)
   4.5.13 \(x y'(x)+\tan (y(x)+x)+x=0\)
   4.5.14 \(x y'(x)=y(x)-x \tan \left (\frac {y(x)}{x}\right )\)
   4.5.15 \(x y'(x)=\left (y(x)^2+1\right ) \left (x^2+\tan ^{-1}(y(x))\right )\)
   4.5.16 \(x y'(x)=x e^{\frac {y(x)}{x}}+y(x)\)
   4.5.17 \(x y'(x)=x e^{\frac {y(x)}{x}}+y(x)+x\)
   4.5.18 \(x y'(x)=y(x) \log (y(x))\)
   4.5.19 \(x y'(x)=y(x) (-\log (y(x))+\log (x)+1)\)
   4.5.20 \(x y'(x)+y(x) (-\log (y(x))-\log (x)+1)=0\)
   4.5.21 \(x y'(x)=y(x)-2 x \tanh \left (\frac {y(x)}{x}\right )\)
   4.5.22 \(n y(x)+x y'(x)=f(x) g\left (x^n y(x)\right )\)
   4.5.23 \(x y'(x)=y(x) f\left (x^m y(x)^n\right )\)
   4.5.24 \((x+1) y'(x)=(3 x+4) x^3+y(x)\)
   4.5.25 \((x+1) y'(x)=2 y(x)+(x+1)^4\)
   4.5.26 \((x+1) y'(x)=n y(x)+e^x (x+1)^{n+1}\)
   4.5.27 \((x+1) y'(x)=a y(x)+b x y(x)^2\)
   4.5.28 \((x+1) y'(x)+(x+1)^4 y(x)^3+y(x)=0\)
   4.5.29 \((x+1) y'(x)=y(x) \left (1-x y(x)^3\right )\)
   4.5.30 \((x+1) y'(x)=(x+1) \sqrt {y(x)+1}+y(x)+1\)
   4.5.31 \((a+x) y'(x)=b x\)
   4.5.32 \((a+x) y'(x)=b x+y(x)\)
   4.5.33 \((a+x) y'(x)+b x^2+y(x)=0\)
   4.5.34 \((a+x) y'(x)=2 (a+x)^5+3 y(x)\)
   4.5.35 \((a+x) y'(x)=b+c y(x)\)
   4.5.36 \((a+x) y'(x)=b x+c y(x)\)
   4.5.37 \((a+x) y'(x)=y(x) (1-a y(x))\)
   4.5.38 \((a-x) y'(x)=y(x)^3 (b+c x)+y(x)\)
   4.5.39 \(2 x y'(x)=2 x^3-y(x)\)
   4.5.40 \(2 x y'(x)+1=y(x)^2+4 i x y(x)\)
   4.5.41 \(2 x y'(x)=y(x) \left (y(x)^2+1\right )\)
   4.5.42 \(2 x y'(x)+y(x) \left (y(x)^2+1\right )=0\)
   4.5.43 \(2 x y'(x)=y(x) \left (-6 y(x)^2+x+1\right )\)
   4.5.44 \(\sqrt {a^2-4 b-4 c y(x)}+a+2 x y'(x)+4 y(x)=0\)
   4.5.45 \((1-2 x) y'(x)=2 (-3 y(x)+16 x+8)\)
   4.5.46 \((2 x+1) y'(x)=4 e^{-y(x)}-2\)
   4.5.47 \(2 (1-x) y'(x)=y(x)+4 \sqrt {1-x} x\)
   4.5.48 \(2 (x+1) y'(x)+(x+1)^4 y(x)^3+2 y(x)=0\)
   4.5.49 \(3 x y'(x)=3 x^{2/3}+(1-3 y(x)) y(x)\)
   4.5.50 \(3 x y'(x)=y(x) \left (x y(x)^3+2\right )\)