Internal problem ID [2440]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.5. page
771
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+2 y^{\prime } x^{2}+\left (x -\frac {3}{4}\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 45
Order:=6; dsolve(x^2*diff(y(x),x$2)+2*x^2*diff(y(x),x)+(x-3/4)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{2} \left (1-\frac {4}{3} x +x^{2}-\frac {8}{15} x^{3}+\frac {2}{9} x^{4}-\frac {8}{105} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (-2+4 x^{2}-\frac {16}{3} x^{3}+4 x^{4}-\frac {32}{15} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 77
AsymptoticDSolveValue[x^2*y''[x]+2*x^2*y'[x]+(x-3/4)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-2 x^{7/2}+\frac {8 x^{5/2}}{3}-2 x^{3/2}+\frac {1}{\sqrt {x}}\right )+c_2 \left (\frac {2 x^{11/2}}{9}-\frac {8 x^{9/2}}{15}+x^{7/2}-\frac {4 x^{5/2}}{3}+x^{3/2}\right ) \]