Internal problem ID [5832]
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: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x \left (x +3\right )^{2} y^{\prime \prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 70
Order:=8; dsolve(x*(x+3)^2*diff(y(x),x$2)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x \left (1+\frac {1}{18} x -\frac {11}{972} x^{2}+\frac {277}{104976} x^{3}-\frac {12539}{18895680} x^{4}+\frac {893821}{5101833600} x^{5}-\frac {13183337}{275499014400} x^{6}+\frac {265861081}{19835929036800} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} \left (\ln \relax (x ) \left (\frac {1}{9} x +\frac {1}{162} x^{2}-\frac {11}{8748} x^{3}+\frac {277}{944784} x^{4}-\frac {12539}{170061120} x^{5}+\frac {893821}{45916502400} x^{6}-\frac {13183337}{2479491129600} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+\left (1-\frac {5}{108} x^{2}+\frac {167}{26244} x^{3}-\frac {13583}{11337408} x^{4}+\frac {1327279}{5101833600} x^{5}-\frac {21146863}{344373768000} x^{6}+\frac {379766273}{24794911296000} x^{7}+\mathrm {O}\left (x^{8}\right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 1.241 (sec). Leaf size: 121
AsymptoticDSolveValue[x*(x+3)^2*y''[x]-y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {x \left (893821 x^5-3385530 x^4+13462200 x^3-57736800 x^2+283435200 x+5101833600\right ) \log (x)}{45916502400}+\frac {24742849 x^6-74732085 x^5+184497750 x^4+52488000 x^3-10628820000 x^2+382637520000 x+688747536000}{688747536000}\right )+c_2 \left (-\frac {13183337 x^7}{275499014400}+\frac {893821 x^6}{5101833600}-\frac {12539 x^5}{18895680}+\frac {277 x^4}{104976}-\frac {11 x^3}{972}+\frac {x^2}{18}+x\right ) \]