4.24 Problems 1151 to 1200

   4.24.1 \(y'(x)+\log \left (y'(x)\right )=x\)
   4.24.2 \(a+x y'(x)+\log \left (y'(x)\right )=0\)
   4.24.3 \(a+x y'(x)+\log \left (y'(x)\right )=y(x)\)
   4.24.4 \(a+b y(x)+x y'(x)+\log \left (y'(x)\right )=0\)
   4.24.5 \(4 x y'(x)+\log \left (y'(x)\right )-2 y(x)=0\)
   4.24.6 \(a \left (x y'(x)-y(x)\right )+\log \left (y'(x)\right )=0\)
   4.24.7 \(a \left (\log \left (y'(x)\right )-y'(x)\right )+y(x)-x=0\)
   4.24.8 \(y'(x)+y(x) \log \left (y'(x)\right )-x y(x)-y(x) \log (y(x))=0\)
   4.24.9 \(-(x+1) y'(x)+y'(x) \log \left (y'(x)\right )+y(x)=0\)
   4.24.10 \(\log \left (x y'(x)-y(x)\right )=y'(x)\)
   4.24.11 \(y'(x) \log \left (\sqrt {a+y'(x)^2}+y'(x)\right )-x y'(x)-\sqrt {y'(x)^2+1}+y(x)=0\)
   4.24.12 \(y'(x) \tan \left (y'(x)\right )+\log \left (\cos \left (y'(x)\right )\right )=y(x)\)
   4.24.13 \(f\left (y'(x)\right )=0\)
   4.24.14 \(f\left (x,y'(x)\right )=0\)
   4.24.15 \(f\left (x y'(x)^2\right )=y(x)-2 x y'(x)\)
   4.24.16 \(f\left (y(x),y'(x)\right )=0\)
   4.24.17 \(f\left (y'(x)\right )+x y'(x)=y(x)\)
   4.24.18 \(f\left (y'(x)\right )+x g\left (y'(x)\right )=y(x)\)
   4.24.19 \(f\left (y'(x),y(x)-x y'(x)\right )=0\)
   4.24.20 \(f\left (x y'(x),y(x)\right )=0\)
   4.24.21 \(x^n f\left (y'(x),\frac {y(x)}{x}\right )=0\)
   4.24.22 \(f\left (y(x) y'(x)+x\right )=y(x)^2 \left (y'(x)^2+1\right )\)
   4.24.23 \(y(x) f\left (\frac {y'(x)}{y(x)},x\right )=0\)
   4.24.24 \(f\left (x,y(x),y'(x)\right )=0\)
   4.24.25 \(y''(x)=0\)
   4.24.26 \(y''(x)=x+\sin (x)\)
   4.24.27 \(y''(x)=\text {c1} \cos (a x)+\text {c2} \sin (b x)\)
   4.24.28 \(y''(x)=e^x x\)
   4.24.29 \(y''(x)=\text {c1} e^{a x}+\text {c2} e^{-b x}\)
   4.24.30 \(y''(x)+y(x)=0\)
   4.24.31 \(y''(x)-y(x)=0\)
   4.24.32 \(y''(x)+y(x)=a x\)
   4.24.33 \(y''(x)+y(x)=a \cos (b x)\)
   4.24.34 \(y''(x)+y(x)=8 \cos (x) \cos (2 x)\)
   4.24.35 \(y''(x)+y(x)=\sec (x)\)
   4.24.36 \(y''(x)+y(x)=a \sin (b x)\)
   4.24.37 \(y''(x)+y(x)=\sin (a x) \sin (b x)\)
   4.24.38 \(y''(x)+y(x)=4 x \sin (x)\)
   4.24.39 \(y''(x)+y(x)=x (\cos (x)-x \sin (x))\)
   4.24.40 \(y''(x)+y(x)=\tan ^2(x)\)
   4.24.41 \(y''(x)+y(x)=e^{-x}\)
   4.24.42 \(y''(x)+y(x)=e^x \left (x^2-1\right )\)
   4.24.43 \(y''(x)+y(x)=e^x \sin (2 x)\)
   4.24.44 \(y''(x)+y(x)=e^{2 x} \cos (x)\)
   4.24.45 \(y''(x)-2 y(x)=0\)
   4.24.46 \(y''(x)-2 y(x)=4 e^{x^2} x^2\)
   4.24.47 \(y''(x)+4 y(x)=0\)
   4.24.48 \(y''(x)+4 y(x)=x \sin ^2(x)\)
   4.24.49 \(y''(x)+4 y(x)=2 \tan (x)\)
   4.24.50 \(y''(x)+4 y(x)=2 \tan (x)\)