Internal problem ID [5851]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.3 SOLUTIONS ABOUT
SINGULAR POINTS. EXERCISES 6.3. Page 255
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }-\left (3+2 x \right ) y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 52
Order:=8; dsolve(2*x*diff(y(x),x$2)-(3+2*x)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {5}{2}} \left (1+\frac {4}{7} x +\frac {4}{21} x^{2}+\frac {32}{693} x^{3}+\frac {80}{9009} x^{4}+\frac {64}{45045} x^{5}+\frac {64}{328185} x^{6}+\frac {1024}{43648605} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} \left (1+\frac {1}{3} x -\frac {1}{6} x^{2}-\frac {1}{6} x^{3}-\frac {5}{72} x^{4}-\frac {7}{360} x^{5}-\frac {1}{240} x^{6}-\frac {11}{15120} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 113
AsymptoticDSolveValue[2*x*y''[x]-(3+2*x)*y'[x]+y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (-\frac {11 x^7}{15120}-\frac {x^6}{240}-\frac {7 x^5}{360}-\frac {5 x^4}{72}-\frac {x^3}{6}-\frac {x^2}{6}+\frac {x}{3}+1\right )+c_1 \left (\frac {1024 x^7}{43648605}+\frac {64 x^6}{328185}+\frac {64 x^5}{45045}+\frac {80 x^4}{9009}+\frac {32 x^3}{693}+\frac {4 x^2}{21}+\frac {4 x}{7}+1\right ) x^{5/2} \]