Internal problem ID [5894]
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. CHAPTER 6 IN REVIEW.
Page 271
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 52
Order:=8; dsolve(x*diff(y(x),x$2)-(x+2)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{3} \left (1+\frac {1}{4} x +\frac {1}{20} x^{2}+\frac {1}{120} x^{3}+\frac {1}{840} x^{4}+\frac {1}{6720} x^{5}+\frac {1}{60480} x^{6}+\frac {1}{604800} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} \left (12+12 x +6 x^{2}+2 x^{3}+\frac {1}{2} x^{4}+\frac {1}{10} x^{5}+\frac {1}{60} x^{6}+\frac {1}{420} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.139 (sec). Leaf size: 94
AsymptoticDSolveValue[x*y''[x]-(x+2)*y'[x]+2*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {x^6}{720}+\frac {x^5}{120}+\frac {x^4}{24}+\frac {x^3}{6}+\frac {x^2}{2}+x+1\right )+c_2 \left (\frac {x^9}{60480}+\frac {x^8}{6720}+\frac {x^7}{840}+\frac {x^6}{120}+\frac {x^5}{20}+\frac {x^4}{4}+x^3\right ) \]