4.29 Problems 1401 to 1450

   4.29.1 \((1-x) y''(x)+x y'(x)-y(x)=0\)
   4.29.2 \((1-x) y''(x)+x y'(x)-y(x)=(1-x)^2\)
   4.29.3 \((3-x) y''(x)-(9-4 x) y'(x)+3 (2-x) y(x)=0\)
   4.29.4 \((a-x) y''(x)-2 y'(x)=0\)
   4.29.5 \((a+x) y''(x)+(\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)=0\)
   4.29.6 \(2 x y''(x)+y'(x)=0\)
   4.29.7 \(a y(x)+2 x y''(x)+y'(x)=0\)
   4.29.8 \(-a y(x)+2 x y''(x)+y'(x)=0\)
   4.29.9 \(y(x) (a+b x)+2 x y''(x)+y'(x)=0\)
   4.29.10 \(-\left (2 x^2+1\right ) y'(x)+2 x y''(x)-x y(x)=0\)
   4.29.11 \((1-2 x) y''(x)-(x+2) y'(x)-y(x)=0\)
   4.29.12 \((1-2 x) y''(x)-(4-3 x) y'(x)+(3-x) y(x)=0\)
   4.29.13 \(4 y''(x)+2 y'(x)+y(x)=0\)
   4.29.14 \(4 y''(x)-2 y'(x)-y(x)=0\)
   4.29.15 \(4 x y''(x)+4 \coth (x) y'(x)+y(x)=0\)
   4.29.16 \(y(x) (a+b x)+16 x y''(x)+8 y'(x)=0\)
   4.29.17 \((a+b x) y''(x)+c y'(x)=0\)
   4.29.18 \((\text {a0}+\text {b0} x) y''(x)+(\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)=0\)
   4.29.19 \((1-x \cot (x)) y''(x)-x y'(x)+y(x)=0\)
   4.29.20 \(x^2 y''(x)=a+b x\)
   4.29.21 \(x^2 y''(x)=2 y(x)\)
   4.29.22 \(x^2 y''(x)=6 y(x)\)
   4.29.23 \(x^2 y''(x)=12 y(x)\)
   4.29.24 \(a y(x)+x^2 y''(x)=0\)
   4.29.25 \(y(x) (a+b x)+x^2 y''(x)=0\)
   4.29.26 \(x^2 y''(x)-\left (2-x^2\right ) y(x)=0\)
   4.29.27 \(x^2 y''(x)-\left (2-x^2\right ) y(x)=x^4\)
   4.29.28 \(x^2 y''(x)-\left (a^2 x^2+2\right ) y(x)=0\)
   4.29.29 \(x^2 y''(x)-\left (6-a^2 x^2\right ) y(x)=0\)
   4.29.30 \(x^2 y''(x)-y(x) \left (a^2 x^2+n (n+1)\right )=0\)
   4.29.31 \(x^2 y''(x)-y(x) \left ((n-1) n-a^2 x^2\right )=0\)
   4.29.32 \(y(x) \left (a+b x+c x^2\right )+x^2 y''(x)=0\)
   4.29.33 \(x^2 y''(x)-y(x) \left ((a-1) a-b x^k\right )=0\)
   4.29.34 \(x^k y(x) \left (a+b x^k\right )+x^2 y''(x)=0\)
   4.29.35 \(-b y(x) \left (a+b x^2\right )+a y'(x)+x^2 y''(x)=0\)
   4.29.36 \(x^2 y''(x)+x y'(x)+y(x)=0\)
   4.29.37 \(x^2 y''(x)+x y'(x)-y(x)=0\)
   4.29.38 \(x^2 y''(x)-x y'(x)+y(x)=0\)
   4.29.39 \(x^2 y''(x)+x y'(x)-y(x)=a x^2\)
   4.29.40 \(x^2 y''(x)-x y'(x)+y(x)=x^2 (x+3)\)
   4.29.41 \(x^2 y''(x)-x y'(x)+y(x)=3 x^3\)
   4.29.42 \(x^2 y''(x)+x y'(x)+y(x)=\log (x)\)
   4.29.43 \(x^2 y''(x)-x y'(x)+2 y(x)=0\)
   4.29.44 \(x^2 y''(x)-x y'(x)+2 y(x)=x \log (x)\)
   4.29.45 \(x^2 y''(x)-x y'(x)-3 y(x)=0\)
   4.29.46 \(a^2 (-y(x))+x^2 y''(x)+x y'(x)=0\)
   4.29.47 \(y(x) (a+b x)+x^2 y''(x)+x y'(x)=0\)
   4.29.48 \(-\left (p^2-x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0\)
   4.29.49 \(-\left (p^2+x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0\)
   4.29.50 \(-\left (p^2+i x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0\)