4.3 Problems 101 to 150

   4.3.1 \(y'(x)=a x+b \sqrt {y(x)}\)
   4.3.2 \(x^3+y'(x)=x \sqrt {x^4+4 y(x)}\)
   4.3.3 \(y'(x)+2 \left (1-x \sqrt {y(x)}\right ) y(x)=0\)
   4.3.4 \(y'(x)=\sqrt {a+b y(x)^2}\)
   4.3.5 \(y'(x)=y(x) \sqrt {a+b y(x)}\)
   4.3.6 \(g(x) (f(x)-y(x)) \sqrt {(y(x)-a) (y(x)-b)}+y'(x)=0\)
   4.3.7 \(y'(x)=\sqrt {X Y}\)
   4.3.8 \(y'(x)=\text {R1}\left (x,\sqrt {X}\right ) \text {R2}\left (y(x),\sqrt {Y}\right )\)
   4.3.9 \(y'(x)=\cos ^2(x) \cos (y(x))\)
   4.3.10 \(y'(x)=\sec ^2(x) \text {Cosy}(y(x)) \cot (y(x))\)
   4.3.11 \(y'(x)=a+b \cos (A x+B y(x))\)
   4.3.12 \(y'(x)=-\left (1-f'(x)\right ) \cos (y(x))+f'(x)-f(x) \sin (y(x))+1\)
   4.3.13 \(g(x) \sin (a y(x))+h(x) \cos (a y(x))+f(x)+y'(x)=0\)
   4.3.14 \(y'(x)=a+b \cos (y(x))\)
   4.3.15 \(x \left (\sin (2 y(x))-x^2 \cos ^2(y(x))\right )+y'(x)=0\)
   4.3.16 \(y'(x)+\tan (x) \sec (x) \cos ^2(y(x))=0\)
   4.3.17 \(y'(x)=\cot (x) \cot (y(x))\)
   4.3.18 \(y'(x)+\cot (x) \cot (y(x))=0\)
   4.3.19 \(y'(x)=\sin (x) (\csc (y(x))-\cot (y(x)))\)
   4.3.20 \(y'(x)=\tan (x) \cot (y(x))\)
   4.3.21 \(y'(x)+\tan (x) \cot (y(x))=0\)
   4.3.22 \(y'(x)+\sin (2 x) \csc (2 y(x))=0\)
   4.3.23 \(y'(x)=\tan (x) (\tan (y(x))+\sec (x) \sec (y(x)))\)
   4.3.24 \(y'(x)=\cos (x) \sec ^2(y(x))\)
   4.3.25 \(y'(x)=\sec ^2(x) \sec ^3(y(x))\)
   4.3.26 \(y'(x)=a+b \sin (y(x))\)
   4.3.27 \(y'(x)=a+b \sin (A x+B y(x))\)
   4.3.28 \(y'(x)=\tan (y(x)) (\cos (x) \sin (y(x))+1)\)
   4.3.29 \(y'(x)+\csc (2 x) \sin (2 y(x))=0\)
   4.3.30 \(f(x)+g(x) \tan (y(x))+y'(x)=0\)
   4.3.31 \(y'(x)=\sqrt {a+b \cos (y(x))}\)
   4.3.32 \(y'(x)=e^{y(x)}+x\)
   4.3.33 \(y'(x)=e^{y(x)+x}\)
   4.3.34 \(y'(x)=e^x \left (a+b e^{-y(x)}\right )\)
   4.3.35 \(y'(x)+y(x) \log (x) \log (y(x))=0\)
   4.3.36 \(y'(x)=x^{m-1} y(x)^{1-n} f\left (a x^m+b y(x)^n\right )\)
   4.3.37 \(y'(x)=a f(y(x))\)
   4.3.38 \(y'(x)=f(a+b x+c y(x))\)
   4.3.39 \(y'(x)=f(x) g(y(x))\)
   4.3.40 \(y'(x)=\text {Csx}(x) y(x) \sec (x)+\sec ^2(x)\)
   4.3.41 \(2 y'(x)+2 \csc ^2(x)=y(x) \csc (x) \sec (x)-y(x)^2 \sec ^2(x)\)
   4.3.42 \(2 y'(x)=2 \sin ^2(y(x)) \tan (y(x))-x \sin (2 y(x))\)
   4.3.43 \(a x+2 y'(x)=\sqrt {a^2 x^2-4 b x^2-4 c y(x)}\)
   4.3.44 \(3 y'(x)=\sqrt {x^2-3 y(x)}+x\)
   4.3.45 \(x y'(x)=\sqrt {a^2-x^2}\)
   4.3.46 \(x y'(x)+y(x)+x=0\)
   4.3.47 \(x^2+x y'(x)-y(x)=0\)
   4.3.48 \(x y'(x)=x^3-y(x)\)
   4.3.49 \(x y'(x)=x^3+y(x)+1\)
   4.3.50 \(x y'(x)=x^m+y(x)\)