4.30 Problems 1451 to 1500

   4.30.1 \(-y(x) \left (p^2-a^2 x^2\right )+x^2 y''(x)+x y'(x)=0\)
   4.30.2 \(-y(x) \left (a+b x+c x^2\right )+x^2 y''(x)+x y'(x)=0\)
   4.30.3 \(-y(x) \left (4 a x^2+n^2-x^4\right )+x^2 y''(x)+x y'(x)=0\)
   4.30.4 \(-y(x) \left (a^2+b^2 x^2+c^2 x^4\right )+x^2 y''(x)+x y'(x)=0\)
   4.30.5 \((m+1) a(m) x^m y(x)+x^2 y''(x)+x y'(x)=0\)
   4.30.6 \((a+x) y'(x)+x^2 y''(x)-y(x)=0\)
   4.30.7 \(x^2 y''(x)-2 x y'(x)+2 y(x)=0\)
   4.30.8 \(x^2 y''(x)-2 x y'(x)+2 y(x)=4 x^3\)
   4.30.9 \(x^2 y''(x)-2 x y'(x)+2 y(x)=x^3 \sin (x)\)
   4.30.10 \(x^2 y''(x)-2 x y'(x)+2 y(x)=2 x \log (x)\)
   4.30.11 \(x^2 y''(x)-2 x y'(x)+2 y(x)=x^5 \log (x)\)
   4.30.12 \(x^2 y''(x)+2 x y'(x)-6 y(x)=0\)
   4.30.13 \(x^2 y''(x)+2 x y'(x)-6 y(x)=2-x\)
   4.30.14 \(\left (a^2 x^2+2\right ) y(x)+x^2 y''(x)-2 x y'(x)=0\)
   4.30.15 \(-y(x) \left (n (n+1)-a^2 x^2\right )+x^2 y''(x)+2 x y'(x)=0\)
   4.30.16 \(y(x) \left (a+b x^2\right )+x^2 y''(x)+2 x y'(x)=0\)
   4.30.17 \(a y(x)+x^2 y''(x)-2 (1-x) y'(x)=0\)
   4.30.18 \(x^2 y''(x)+3 x y'(x)+y(x)=0\)
   4.30.19 \(x^2 y''(x)+3 x y'(x)+y(x)=x\)
   4.30.20 \(x^2 y''(x)+3 x y'(x)+y(x)=a-x+x \log (x)\)
   4.30.21 \(x^2 y''(x)-3 x y'(x)+4 y(x)=0\)
   4.30.22 \(x^2 y''(x)-3 x y'(x)+4 y(x)=5 x\)
   4.30.23 \(x^2 y''(x)-3 x y'(x)-5 y(x)=0\)
   4.30.24 \(x^2 y''(x)-3 x y'(x)-5 y(x)=x^2 \log (x)\)
   4.30.25 \(x^2 y''(x)+4 x y'(x)+2 y(x)=0\)
   4.30.26 \(x^2 y''(x)+4 x y'(x)+2 y(x)=e^x\)
   4.30.27 \(x^2 y''(x)+4 x y'(x)+2 y(x)=\log (x+1)\)
   4.30.28 \(x^2 y''(x)-4 x y'(x)+6 y(x)=0\)
   4.30.29 \(x^2 y''(x)-4 x y'(x)+6 y(x)=x^2 \left (x^2-1\right )\)
   4.30.30 \(x^2 y''(x)+\left (2-x^2\right ) y(x)+4 x y'(x)=0\)
   4.30.31 \(x^2 y''(x)+\left (x^2+6\right ) y(x)+4 x y'(x)=0\)
   4.30.32 \(x^2 y''(x)+5 x y'(x)+13 y(x)=0\)
   4.30.33 \(x^2 y''(x)-7 x y'(x)+16 y(x)=0\)
   4.30.34 \(y(x) \left (a (a+1)+b^2 x^2\right )-2 a x y'(x)+x^2 y''(x)=0\)
   4.30.35 \(\text {a1} x y'(x)+\text {a2} y(x)+x^2 y''(x)=0\)
   4.30.36 \(\text {a1} x y'(x)+y(x) (\text {a2}+\text {b2} x)+x^2 y''(x)=0\)
   4.30.37 \(\text {a1} x y'(x)+y(x) \left (\text {a2}+\text {b2} x^2\right )+x^2 y''(x)=0\)
   4.30.38 \(\text {a1} x y'(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )+x^2 y''(x)=0\)
   4.30.39 \(a x y'(x)+y(x) \left (b+c x^3\right )+x^2 y''(x)=0\)
   4.30.40 \(a x y'(x)+x^2 y(x) \left (\text {a1}+\text {b1} x^2\right )+x^2 y''(x)=0\)
   4.30.41 \(a x y'(x)+y(x) \left (b+c x^{2 k}\right )+x^2 y''(x)=0\)
   4.30.42 \((a+b x) y'(x)+c y(x)+x^2 y''(x)=0\)
   4.30.43 \(-2 a x y'(x)+a (a+1) y(x)+x^2 y''(x)=0\)
   4.30.44 \(-2 a x y'(x)+a (a+1) y(x)+x^2 y''(x)=e^x x^{a+2}\)
   4.30.45 \(y(x) \left (a (a+1)+b^2 x^2\right )-2 a x y'(x)+x^2 y''(x)=0\)
   4.30.46 \(y(x) (a+b x)+2 a x y'(x)+x^2 y''(x)=0\)
   4.30.47 \(x^2 y''(x)-x^2 y'(x)-2 x^2 y(x)=2 x^2 \log (x)+x+1\)
   4.30.48 \(y(x) \left (a+b x^2\right )+x^2 y''(x)+x^2 y'(x)=0\)
   4.30.49 \(x^2 y''(x)-\left (1-x^2\right ) y'(x)-y(x)=0\)
   4.30.50 \(x^2 y''(x)+(1-x) x y'(x)-(1-x) y(x)=0\)