4.33 Problems 1601 to 1650

   4.33.1 \(x (\text {a0}+x) y''(x)+(\text {a1}+\text {b1} x) y'(x)+\text {a2} y(x)=0\)
   4.33.2 \(-4 (a+x) y'(x)+(\text {a0}+x)^2 y''(x)+6 y(x)=0\)
   4.33.3 \(2 x^2 y''(x)-x y'(x)+y(x)=x^2\)
   4.33.4 \(2 x^2 y''(x)+x y'(x)-3 y(x)=0\)
   4.33.5 \(2 x^2 y''(x)-(2 x+7) x y'(x)+2 (x+5) y(x)=0\)
   4.33.6 \(2 x^2 y''(x)-(1-4 x) x y'(x)-2 (1-3 x) y(x)=0\)
   4.33.7 \(2 x^2 y''(x)-(1-4 x) x y'(x)-2 (1-3 x) y(x)=x^3 (x+1)\)
   4.33.8 \(\left (2 x^2+1\right ) y''(x)+3 x y'(x)-3 y(x)=0\)
   4.33.9 \(2 a^2 y(x)+2 \left (1-x^2\right ) y''(x)-x y'(x)=0\)
   4.33.10 \(2 x (x+1) y''(x)+y'(x)-4 y(x)=0\)
   4.33.11 \(2 (1-x) x y''(x)+(x+1) y'(x)-y(x)=0\)
   4.33.12 \(2 (1-x) x y''(x)+(1-x) y'(x)+y(x)=0\)
   4.33.13 \(2 (1-x) x y''(x)+(1-2 x) y'(x)-2 y(x)=0\)
   4.33.14 \(2 (1-x) x y''(x)+(1-2 x) y'(x)+8 y(x)=0\)
   4.33.15 \(a y(x)+2 (1-x) x y''(x)-(1-2 x) y'(x)=0\)
   4.33.16 \(y(x) (a+b x)+2 (1-x) x y''(x)+(1-2 x) y'(x)=0\)
   4.33.17 \(2 a (a+1) y(x)+2 (1-x) x y''(x)-(3 x+1) y'(x)=0\)
   4.33.18 \((1-2 x) (1-x) y''(x)+2 (1-2 x) y'(x)+4 y(x)=0\)
   4.33.19 \((1-2 x) (1-x) y''(x)+2 (3-4 x) y'(x)+12 y(x)=0\)
   4.33.20 \(2 (x+1)^2 y''(x)-(x+1) y'(x)+y(x)=0\)
   4.33.21 \(2 (x+1)^2 y''(x)-(x+1) y'(x)+y(x)=x\)
   4.33.22 \(4 x^2 y''(x)+y(x)=0\)
   4.33.23 \(4 x^2 y''(x)+y(x)=\sqrt {x}\)
   4.33.24 \(y(x) \left (4 k x-4 p^2-x^2+1\right )+4 x^2 y''(x)=0\)
   4.33.25 \(\left (4 a^2 x^2+1\right ) y(x)+4 x^2 y''(x)=0\)
   4.33.26 \(-\left (a^2-x\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0\)
   4.33.27 \(4 x^2 y''(x)-\left (4 x^2+1\right ) y(x)+4 x y'(x)=4 e^x x^{3/2}\)
   4.33.28 \(-\left ((2 n+1)^2-4 x^2\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0\)
   4.33.29 \(-\left (a^2 x^2+1\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0\)
   4.33.30 \(4 x^2 y''(x)-8 x y'(x)+5 y(x)=0\)
   4.33.31 \(4 x^2 y''(x)-2 (x+2) x y'(x)+(x+3) y(x)=0\)
   4.33.32 \(4 x^2 y''(x)-\left (-4 x^2+4 x+1\right ) y(x)+4 (1-2 x) x y'(x)=0\)
   4.33.33 \(4 x^3 y'(x)+4 x^2 y''(x)-\left (3-2 x^2\right ) y(x)=0\)
   4.33.34 \(4 x^3 y'(x)+4 x^2 y''(x)+\left (x^4+2 x^2+1\right ) y(x)=0\)
   4.33.35 \(\left (a+x^4+2 x^2\right ) y(x)+4 x^3 y'(x)+4 x^2 y''(x)=0\)
   4.33.36 \(4 \left (1-x^2\right ) y''(x)-8 x y'(x)-y(x)=0\)
   4.33.37 \(-\left (4 p^2+1\right ) y(x)+4 \left (1-x^2\right ) y''(x)-8 x y'(x)=0\)
   4.33.38 \(4 \left (x^2+1\right ) y''(x)=x^2+4 x y'(x)\)
   4.33.39 \(4 a x y'(x)-a (a+2) y(x)+4 \left (1-x^2\right ) y''(x)=0\)
   4.33.40 \(4 (1-x) x y''(x)+2 (1-x) y'(x)+y(x)=0\)
   4.33.41 \(y(x) (a+b x)+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0\)
   4.33.42 \(y(x) \left (a+b x+c x^2\right )+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0\)
   4.33.43 \(y(x) \left (\sum _{m=0}^n a(m) x^m\right )+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0\)
   4.33.44 \(-(k-p) (k+p+1) y(x)+2 (1-(3-2 k) x) y'(x)+4 (1-x) x y''(x)=0\)
   4.33.45 \(2 (a x+1) y'(x)+y(x) \left (b+k^2 x\right )+4 (1-x) x y''(x)=0\)
   4.33.46 \((2 x+1)^2 y''(x)-2 (2 x+1) y'(x)-12 y(x)=0\)
   4.33.47 \((2 x+1)^2 y''(x)-2 (2 x+1) y'(x)-12 y(x)=3 x+1\)
   4.33.48 \((1-3 x)^2 y''(x)-3 (1-3 x) y'(x)-9 y(x)=0\)
   4.33.49 \(16 x^2 y''(x)+(4 x+3) y(x)=0\)
   4.33.50 \(16 x^2 y''(x)+32 x y'(x)-(4 x+5) y(x)=0\)