Internal problem ID [2408]
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 11.4. page
758
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y^{\prime }}{1-x}+y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
Order:=6; dsolve(diff(y(x),x$2)+1/(1-x)*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {1}{6} x^{3}+\frac {1}{24} x^{4}+\frac {1}{60} x^{5}\right ) y \relax (0)+\left (x -\frac {1}{2} x^{2}-\frac {1}{12} x^{4}+\frac {1}{24} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 56
AsymptoticDSolveValue[y''[x]+1/(1-x)*y'[x]+x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^5}{60}+\frac {x^4}{24}-\frac {x^3}{6}+1\right )+c_2 \left (\frac {x^5}{24}-\frac {x^4}{12}-\frac {x^2}{2}+x\right ) \]