4.32 Problems 1551 to 1600

   4.32.1 \(p (2 k+p) y(x)-(2 k+1) x y'(x)+\left (1-x^2\right ) y''(x)=0\)
   4.32.2 \(n y(x) (a+b+n+1)+(-x (a+b+2)-a+b) y'(x)+\left (1-x^2\right ) y''(x)=0\)
   4.32.3 \(-(k-p) (k+p+1) y(x)-2 (k+1) x y'(x)+\left (1-x^2\right ) y''(x)=0\)
   4.32.4 \(-2 a x y'(x)+(1-a) a y(x)+\left (1-x^2\right ) y''(x)=0\)
   4.32.5 \(a x y'(x)-(2-a) y(x)+\left (x^2+1\right ) y''(x)=0\)
   4.32.6 \(a x y'(x)+b y(x)+\left (1-x^2\right ) y''(x)=0\)
   4.32.7 \(a x y'(x)+y(x) \left (\text {a0}+\text {b0} x+\text {c0} x^2\right )+\left (1-x^2\right ) y''(x)=0\)
   4.32.8 \((a+b x) y'(x)+c y(x)+\left (1-x^2\right ) y''(x)=0\)
   4.32.9 \(\left (a^2-x^2\right ) y''(x)+y(x) \left (b^2+c^2 x^2\right )-x y'(x)=0\)
   4.32.10 \(\left (a^2-x^2\right ) y''(x)-8 x y'(x)-12 y(x)=0\)
   4.32.11 \((1-x) x y''(x)+2 y'(x)+y(x)=0\)
   4.32.12 \((1-x) x y''(x)-2 y'(x)+2 y(x)=0\)
   4.32.13 \((1-x) x y''(x)+2 y'(x)+6 y(x)=0\)
   4.32.14 \((1-x) x y''(x)-2 y'(x)+6 y(x)=0\)
   4.32.15 \((1-x) x y''(x)+3 y'(x)+2 y(x)=0\)
   4.32.16 \((1-x) x y''(x)-3 y'(x)+2 y(x)=0\)
   4.32.17 \((1-x) x y''(x)-3 y'(x)+2 y(x)=x \left (3 x^3+1\right )\)
   4.32.18 \(-a y'(x)+(1-x) x y''(x)+2 y(x)=0\)
   4.32.19 \(x (x+1) y''(x)+(1-x) y'(x)+y(x)=0\)
   4.32.20 \((1-x) x y''(x)-(x+1) y'(x)+y(x)=0\)
   4.32.21 \((1-x) x y''(x)-(x+4) y'(x)+4 y(x)=0\)
   4.32.22 \((1-x) x y''(x)+2 x y'(x)-2 y(x)=0\)
   4.32.23 \((1-x) x y''(x)+(1-2 x) y'(x)+6 y(x)=0\)
   4.32.24 \(p (p+1) y(x)+(1-x) x y''(x)+(1-2 x) y'(x)=0\)
   4.32.25 \((1-x) x y''(x)+(1-x) y'(x)+2 y(x)=0\)
   4.32.26 \((1-x) x y''(x)-3 x y'(x)-y(x)=0\)
   4.32.27 \(x (x+1) y''(x)+(3 x+2) y'(x)+y(x)=0\)
   4.32.28 \((1-x) x y''(x)+(1-4 x) y'(x)-2 y(x)=0\)
   4.32.29 \((1-x) x y''(x)-2 (2 x+1) y'(x)-2 y(x)=0\)
   4.32.30 \((1-x) x y''(x)-2 (1-2 x) y'(x)-6 y(x)=0\)
   4.32.31 \((p-k) (k+p+1) y(x)+(k+1) (1-2 x) y'(x)+(1-x) x y''(x)=0\)
   4.32.32 \((c-(a+1) x) y'(x)+n (a+n) y(x)+(1-x) x y''(x)=0\)
   4.32.33 \((a+b x) y'(x)+c y(x)+x (x+1) y''(x)=0\)
   4.32.34 \(y'(x) (c-x (a+b+1))-a b y(x)+(1-x) x y''(x)=0\)
   4.32.35 \(-(a-(2-a) x) y'(x)-a y(x)+x (x+1) y''(x)=0\)
   4.32.36 \(-(a-(2-a) x) y'(x)-a y(x)+x (x+1) y''(x)=0\)
   4.32.37 \((a+b x) y'(x)+c y(x)+(1-x) x y''(x)=0\)
   4.32.38 \(y(x) \left (\sum _{m=0}^n a(m) x^m\right )+a (1-2 x) y'(x)+x (x+1) y''(x)=0\)
   4.32.39 \(\left (-x^2-x+2\right ) y''(x)+(1-x) x y'(x)+x (6 x+7) y(x)=0\)
   4.32.40 \((2-x) x y''(x)+2 (1-x) y'(x)+2 y(x)=0\)
   4.32.41 \(-\left (2-x^2\right ) y'(x)+(2-x) x y''(x)+2 (1-x) y(x)=0\)
   4.32.42 \((1-x)^2 y''(x)-4 (1-x) y'(x)+2 y(x)=0\)
   4.32.43 \((1-x)^2 y''(x)-4 (1-x) y'(x)+2 y(x)=\cos (x)\)
   4.32.44 \((x+1)^2 y''(x)-4 (x+1) y'(x)+6 y(x)=0\)
   4.32.45 \((x+1)^2 y''(x)-4 (x+1) y'(x)+6 y(x)=x\)
   4.32.46 \(-\left (-x^2-x+1\right ) y'(x)+(x+1)^2 y''(x)-(x+2) y(x)=0\)
   4.32.47 \((1-x)^2 y''(x)-2 (1-x)^2 y'(x)+(1-x)^2 y(x)=e^x\)
   4.32.48 \(\left (x^2+3 x+4\right ) y''(x)+\left (x^2+x+1\right ) y'(x)-(2 x+3) y(x)=0\)
   4.32.49 \((x+2)^2 y''(x)-(x+2) y'(x)+2 y(x)=0\)
   4.32.50 \((2-x)^2 y''(x)+(2-x) y'(x)-3 y(x)=0\)