Internal problem ID [735]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 5.3, Series Solutions Near an Ordinary Point, Part II. page 269
Problem number: 3.
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 }+\left (x +1\right ) y^{\prime }+3 \ln \relax (x ) y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2, y^{\prime }\relax (1) = 0] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
Order:=6; dsolve([x^2*diff(y(x),x$2)+(1+x)*diff(y(x),x)+3*ln(x)*y(x)=0,y(1) = 2, D(y)(1) = 0],y(x),type='series',x=1);
\[ y \relax (x ) = 2-\left (x -1\right )^{3}+\frac {7}{4} \left (x -1\right )^{4}-\frac {49}{20} \left (x -1\right )^{5}+\mathrm {O}\left (\left (x -1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 30
AsymptoticDSolveValue[{x^2*y''[x]+(1+x)*y'[x]+3*Log[x]*y[x]==0,{y[1]==2,y'[1]==0}},y[x],{x,1,5}]
\[ y(x)\to -\frac {49}{20} (x-1)^5+\frac {7}{4} (x-1)^4-(x-1)^3+2 \]