Internal problem ID [725]
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: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -3, y^{\prime }\relax (0) = 2] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
Order:=6; dsolve([(1-x)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(0) = -3, D(y)(0) = 2],y(x),type='series',x=0);
\[ y \relax (x ) = -3+2 x -\frac {3}{2} x^{2}-\frac {1}{2} x^{3}-\frac {1}{8} x^{4}-\frac {1}{40} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 36
AsymptoticDSolveValue[{(1-x)*y''[x]+x*y'[x]-y[x]==0,{y[0]==-3,y'[0]==2}},y[x],{x,0,5}]
\[ y(x)\to -\frac {x^5}{40}-\frac {x^4}{8}-\frac {x^3}{2}-\frac {3 x^2}{2}+2 x-3 \]