4.28 Problems 1351 to 1400

   4.28.1 \(\left (4 a-x^2+2\right ) y(x)+4 y''(x)=0\)
   4.28.2 \(4 y''(x)-8 y'(x)+3 y(x)=0\)
   4.28.3 \(x y''(x)+y(x)=0\)
   4.28.4 \((a+x) y(x)+x y''(x)=0\)
   4.28.5 \(x y''(x)+y'(x)=0\)
   4.28.6 \(x y''(x)+y'(x)=x^n\)
   4.28.7 \(x y''(x)+y'(x)-y(x)=0\)
   4.28.8 \(x y''(x)+y'(x)-(x+1) y(x)=0\)
   4.28.9 \(4 x^3 y(x)+x y''(x)-y'(x)=0\)
   4.28.10 \(-a^2 x^3 y(x)+x y''(x)-y'(x)=0\)
   4.28.11 \(x^3 \left (e^{x^2}-k^2\right ) y(x)+x y''(x)-y'(x)=0\)
   4.28.12 \(x y''(x)+2 y'(x)=0\)
   4.28.13 \(x y''(x)+2 y'(x)=0\)
   4.28.14 \(x y''(x)+2 y'(x)-x y(x)=e^x\)
   4.28.15 \(a x y(x)+x y''(x)+2 y'(x)=0\)
   4.28.16 \(a x^2 y(x)+x y''(x)+2 y'(x)=0\)
   4.28.17 \(a y'(x)+x y''(x)=0\)
   4.28.18 \((a+1) y'(x)+x y''(x)+y(x)=0\)
   4.28.19 \((1-a) y'(x)+x y''(x)+y(x)=0\)
   4.28.20 \((a+1) y'(x)+x y''(x)-y(x)=0\)
   4.28.21 \(2 n y'(x)+x y''(x)-y(x)=0\)
   4.28.22 \(a y'(x)+b y(x)+x y''(x)=0\)
   4.28.23 \(a y'(x)+b x y(x)+x y''(x)=0\)
   4.28.24 \(a y'(x)+y(x) (\text {b1}+\text {b2} x)+x y''(x)=0\)
   4.28.25 \(a y'(x)+y(x) \left (\text {a1}+\text {b1} x+\text {c1} x^2\right )+x y''(x)=0\)
   4.28.26 \(a y'(x)+b x^k y(x)+x y''(x)=0\)
   4.28.27 \(x y''(x)-(x+1) y'(x)+y(x)=0\)
   4.28.28 \(n y(x)+x y''(x)+(1-x) y'(x)=0\)
   4.28.29 \((k-x+1) y'(x)+n y(x)+x y''(x)=0\)
   4.28.30 \(x y''(x)-(x+1) y'(x)+2 (1-x) y(x)=0\)
   4.28.31 \(x y''(x)-(2-x) y'(x)-y(x)=0\)
   4.28.32 \(x y''(x)-(x+3) y'(x)+y(x)=0\)
   4.28.33 \(x y''(x)-(x+3) y'(x)+3 y(x)=0\)
   4.28.34 \((a+x) y'(x)+b y(x)+x y''(x)=0\)
   4.28.35 \(-a y(x)+(c-x) y'(x)+x y''(x)=0\)
   4.28.36 \(x y''(x)+(1-2 x) y'(x)-(1-x) y(x)=0\)
   4.28.37 \(x y''(x)-(2 x+1) y'(x)+(x+1) y(x)=0\)
   4.28.38 \(x y''(x)-(2 x+1) y'(x)+(x+1) y(x)=x^2-x-1\)
   4.28.39 \((a+b x) y'(x)+c y(x)+x y''(x)=0\)
   4.28.40 \((\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)+x y''(x)=0\)
   4.28.41 \(-2 (a+b x) y'(x)+y(x) (2 a+b x)+x y''(x)=0\)
   4.28.42 \(y'(x) (x (a+b)+m+n)+y(x) (a b x+a n+b m)+x y''(x)=0\)
   4.28.43 \(x y''(x)-\left (1-x^2\right ) y'(x)=0\)
   4.28.44 \(-\left (4-x^2\right ) y'(x)+x y''(x)+2 x y(x)=0\)
   4.28.45 \(x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=0\)
   4.28.46 \(-8 x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=0\)
   4.28.47 \(-8 x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=4 e^{-x^2} x^3\)
   4.28.48 \(\left (4 x^2+1\right ) y'(x)+4 x \left (x^2+1\right ) y(x)+x y''(x)=0\)
   4.28.49 \(-\left (1-2 a x^3\right ) y'(x)+a x^2 \left (a x^3+1\right ) y(x)+x y''(x)=0\)
   4.28.50 \((x f(x)+2) y'(x)+f(x) y(x)+x y''(x)=0\)