Internal problem ID [732]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 5.2, Series Solutions Near an Ordinary Point, Part I. page 263
Problem number: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
Order:=6; dsolve([(1-x)*diff(y(x),x$2)+x*diff(y(x),x)-2*y(x)=0,y(0) = 0, D(y)(0) = 1],y(x),type='series',x=0);
\[ y \relax (x ) = x +\frac {1}{6} x^{3}+\frac {1}{12} x^{4}+\frac {1}{24} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 26
AsymptoticDSolveValue[{(1-x)*y''[x]+x*y'[x]-2*y[x]==0,{y[0]==0,y'[0]==1}},y[x],{x,0,5}]
\[ y(x)\to \frac {x^5}{24}+\frac {x^4}{12}+\frac {x^3}{6}+x \]