Internal problem ID [5271]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 3. Linear equations with variable coefficients. Page 130
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (x -1\right )^{2} y^{\prime }-\left (x -1\right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1, y^{\prime }\relax (1) = 0] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
Order:=6; dsolve([diff(y(x),x$2)+(x-1)^2*diff(y(x),x)-(x-1)*y(x)=0,y(1) = 1, D(y)(1) = 0],y(x),type='series',x=1);
\[ y \relax (x ) = 1+\frac {1}{6} \left (x -1\right )^{3}+\mathrm {O}\left (\left (x -1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 14
AsymptoticDSolveValue[{y''[x]+(x-1)^2*y'[x]-(x-1)*y[x]==0,{y[1]==1,y'[1]==0}},y[x],{x,1,5}]
\[ y(x)\to \frac {1}{6} (x-1)^3+1 \]