Internal problem ID [4804]
Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G.
Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.2 page
239
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: 0.026 (sec). Leaf size: 58
Order:=6; dsolve(x*(x+3)^2*diff(y(x),x$2)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x \left (1+\frac {1}{18} x -\frac {11}{972} x^{2}+\frac {277}{104976} x^{3}-\frac {12539}{18895680} x^{4}+\frac {893821}{5101833600} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \relax (x ) \left (\frac {1}{9} x +\frac {1}{162} x^{2}-\frac {11}{8748} x^{3}+\frac {277}{944784} x^{4}-\frac {12539}{170061120} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (1-\frac {5}{108} x^{2}+\frac {167}{26244} x^{3}-\frac {13583}{11337408} x^{4}+\frac {1327279}{5101833600} x^{5}+\mathrm {O}\left (x^{6}\right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 87
AsymptoticDSolveValue[x*(x+3)^2*y''[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x \left (277 x^3-1188 x^2+5832 x+104976\right ) \log (x)}{944784}+\frac {3037 x^4+864 x^3-174960 x^2+6298560 x+11337408}{11337408}\right )+c_2 \left (-\frac {12539 x^5}{18895680}+\frac {277 x^4}{104976}-\frac {11 x^3}{972}+\frac {x^2}{18}+x\right ) \]