Internal problem ID [2428]
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: Example 11.5.2 page 763.
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 }-x \left (x +3\right ) y^{\prime }+\left (-x +4\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 69
Order:=6; dsolve(x^2*diff(y(x),x$2)-x*(3+x)*diff(y(x),x)+(4-x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\left (\left (-5\right ) x -\frac {29}{4} x^{2}-\frac {173}{36} x^{3}-\frac {193}{96} x^{4}-\frac {1459}{2400} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}+\left (\ln \relax (x ) c_{2}+c_{1}\right ) \left (1+3 x +3 x^{2}+\frac {5}{3} x^{3}+\frac {5}{8} x^{4}+\frac {7}{40} x^{5}+\mathrm {O}\left (x^{6}\right )\right )\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 118
AsymptoticDSolveValue[x^2*y''[x]-x*(3+x)*y'[x]+(4-x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {7 x^5}{40}+\frac {5 x^4}{8}+\frac {5 x^3}{3}+3 x^2+3 x+1\right ) x^2+c_2 \left (\left (-\frac {1459 x^5}{2400}-\frac {193 x^4}{96}-\frac {173 x^3}{36}-\frac {29 x^2}{4}-5 x\right ) x^2+\left (\frac {7 x^5}{40}+\frac {5 x^4}{8}+\frac {5 x^3}{3}+3 x^2+3 x+1\right ) x^2 \log (x)\right ) \]