4.35 Problems 1701 to 1750

   4.35.1 \(2 (2-x) x^2 y''(x)-(4-x) x y'(x)+(3-x) y(x)=0\)
   4.35.2 \(x \left (3 x^2+1\right ) y''(x)+2 y'(x)-6 x y(x)=0\)
   4.35.3 \(4 (x+1) x^2 y''(x)-4 x^2 y'(x)+(3 x+1) y(x)=0\)
   4.35.4 \(x^2 (a+b x) y''(x)-2 x (2 a+b x) y'(x)+2 y(x) (3 a+b x)=0\)
   4.35.5 \(y(x) (a+b x)+4 (1-x) x y''(x)+2 (1-3 x) (1-x) y'(x)=0\)
   4.35.6 \(4 (1-x) x (1-a x) y''(x)+y'(x) \left (\text {a0}+\text {a1} x+\text {a2} x^2\right )+y(x) \left (\text {b0}+\text {b1} x^2\right )=0\)
   4.35.7 \(a^2 y(x)+x^4 y''(x)=0\)
   4.35.8 \(x^4 y''(x)+\left (1-2 x^2\right ) y(x)=0\)
   4.35.9 \(x^4 y''(x)-\left (2 x^2+1\right ) y(x)=0\)
   4.35.10 \(\left (e^{2/x}-a^2\right ) y(x)+x^4 y''(x)=0\)
   4.35.11 \(x^4 y''(x)+x y'(x)-2 y(x)=0\)
   4.35.12 \(x^4 y''(x)-2 x^2 y'(x)+(2 x+1) y(x)=0\)
   4.35.13 \(x^4 y''(x)+x^3 y'(x)+y(x)=0\)
   4.35.14 \(x^4 y''(x)+x^3 y'(x)-(x+1) y(x)=0\)
   4.35.15 \(y(x) \left (a+b x^2+c x^4\right )+x^4 y''(x)+x^3 y'(x)=0\)
   4.35.16 \(x^4 y''(x)+\left (x^2+1\right ) x y'(x)+y(x)=0\)
   4.35.17 \(x^4 y''(x)-\left (1-x^2\right ) x y'(x)+\left (1-x^2\right ) y(x)=0\)
   4.35.18 \(a^2 y(x)+x^4 y''(x)+2 x^3 y'(x)=0\)
   4.35.19 \(x^4 y''(x)+\left (2 x^2+1\right ) x y'(x)-y(x)=0\)
   4.35.20 \(2 x^2 (a+x) y'(x)+b y(x)+x^4 y''(x)=0\)
   4.35.21 \(\left (x^3+1\right ) x y''(x)-\left (1-x^3\right ) y'(x)+x^2 (-y(x))=0\)
   4.35.22 \(x^3 \left (-y'(x)\right )+\left (1-x^2\right ) x^2 y''(x)-2 y(x)=0\)
   4.35.23 \(\left (1-x^2\right ) x^2 y''(x)-\left (2-x^2\right ) x y'(x)+\left (2-x^2\right ) y(x)=0\)
   4.35.24 \(a (a+1) y(x)-2 x^3 y'(x)+\left (1-x^2\right ) x^2 y''(x)=0\)
   4.35.25 \(\left (x^2+1\right )^2 y''(x)+2 x \left (x^2+1\right ) y'(x)+y(x)=0\)
   4.35.26 \(\left (x^2+1\right )^2 y''(x)+2 x \left (x^2+1\right ) y'(x)+4 y(x)=0\)
   4.35.27 \(a^2 (-y(x))+\left (x^2+1\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)
   4.35.28 \(-y(x) \left (m^2-n (n+1) \left (1-x^2\right )\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)
   4.35.29 \(-y(x) \left (k^2-p (p+1) \left (1-x^2\right )\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)
   4.35.30 \(-y(x) \left (a^2-k \left (1-x^2\right )\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)
   4.35.31 \(y(x) \left (\text {a0}+\text {a2} x^2+\text {a4} x^4\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)
   4.35.32 \(y(x) \left (\sum _{m=0}^n a(m) x^m\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)
   4.35.33 \(a x \left (1-x^2\right ) y'(x)+b y(x)+\left (x^2+1\right )^2 y''(x)=0\)
   4.35.34 \(\text {a1} x \left (1-x^2\right ) y'(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )+\left (1-x^2\right )^2 y''(x)=0\)
   4.35.35 \(x^2 \left (a^2+x^2\right )^2 y''(x)+x \left (a^2+2 x^2\right ) y'(x)+b^2 y(x)=0\)
   4.35.36 \(\left (a^2+x^2\right )^2 y''(x)+2 x \left (a^2+2 x^2\right ) y'(x)-y(x) \left (\text {a0}+\text {a2} x^2+\text {a4} x^4\right )=0\)
   4.35.37 \(\left (a^2-x^2\right )^2 y''(x)-2 x \left (a^2-x^2\right ) y'(x)+y(x) \left (\text {a0}+\text {a2} x^2+\text {a4} x^4\right )=0\)
   4.35.38 \(\left (a^2+x^2\right )^2 \left (b^2+x^2\right ) y''(x)+x \left (\text {a0}+\text {b0} x^2\right ) y'(x)+y(x) \left (\text {a1}+\text {b1} x^2\right )=0\)
   4.35.39 \(\left (a^2-x^2\right )^2 \left (b^2-x^2\right ) y''(x)+x \left (\text {a0}+\text {b0} x^2\right ) y'(x)+y(x) \left (\text {a1}+\text {b1} x^2+\text {c1} x^4\right )=0\)
   4.35.40 \((1-x) x (x+1)^2 y''(x)+2 (3-x) x (x+1) y'(x)-2 (1-x) y(x)=0\)
   4.35.41 \(y(x) \left (a+b x+c x^2\right )+(1-x)^2 x^2 y''(x)=0\)
   4.35.42 \((1-x)^2 x^2 y''(x)+(1-2 x) (1-x) x y'(x)-y(x)=0\)
   4.35.43 \((1-x) x (\text {a1}+\text {b2} x) y'(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )+(1-x)^2 x^2 y''(x)=0\)
   4.35.44 \(y(x) \left (\sum _{m=0}^n a(m) x^m\right )+(1-x)^2 x^2 y''(x)+(1-2 x) (1-x) x y'(x)=0\)
   4.35.45 \(x^2 (a-x)^2 y''(x)+b y(x)=0\)
   4.35.46 \((a-x)^2 (b-x)^2 y''(x)=k^2 y(x)\)
   4.35.47 \((a-x) (A+2 x) (b-x) y'(x)+(a-x)^2 (b-x)^2 y''(x)+B y(x)=0\)
   4.35.48 \((a-x)^4 y''(x)-2 (a-x)^3 y'(x)-y(x)=0\)
   4.35.49 \((1-2 x) (1-x) x^2 y''(x)+2 (2-3 x) x y'(x)+2 (3 x+1) y(x)=0\)
   4.35.50 \((1-2 x) (1-x) x^2 y''(x)+2 (1-2 x) (2-x) x y'(x)+2 (1-x) y(x)=0\)