Internal problem ID [5719]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Section 4.6. Gauss’s Hypergeometric
Equation. Page 187
Problem number: 2(x).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y=0} \end {gather*} With the expansion point for the power series method at \(x = -1\).
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 54
Order:=8; dsolve((x^2-1)*diff(y(x),x$2)+(5*x+4)*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=-1);
\[ y \relax (x ) = c_{1} \sqrt {x +1}\, \left (1+\frac {25}{12} \left (x +1\right )+\frac {245}{96} \left (x +1\right )^{2}+\frac {315}{128} \left (x +1\right )^{3}+\frac {4235}{2048} \left (x +1\right )^{4}+\frac {13013}{8192} \left (x +1\right )^{5}+\frac {75075}{65536} \left (x +1\right )^{6}+\frac {206635}{262144} \left (x +1\right )^{7}+\mathrm {O}\left (\left (x +1\right )^{8}\right )\right )+c_{2} \left (1+4 \left (x +1\right )+6 \left (x +1\right )^{2}+\frac {32}{5} \left (x +1\right )^{3}+\frac {40}{7} \left (x +1\right )^{4}+\frac {32}{7} \left (x +1\right )^{5}+\frac {112}{33} \left (x +1\right )^{6}+\frac {1024}{429} \left (x +1\right )^{7}+\mathrm {O}\left (\left (x +1\right )^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 139
AsymptoticDSolveValue[(x^2-1)*y''[x]+(5*x+4)*y'[x]+4*y[x]==0,y[x],{x,-1,7}]
\[ y(x)\to c_1 \sqrt {x+1} \left (\frac {206635 (x+1)^7}{262144}+\frac {75075 (x+1)^6}{65536}+\frac {13013 (x+1)^5}{8192}+\frac {4235 (x+1)^4}{2048}+\frac {315}{128} (x+1)^3+\frac {245}{96} (x+1)^2+\frac {25 (x+1)}{12}+1\right )+c_2 \left (\frac {1024}{429} (x+1)^7+\frac {112}{33} (x+1)^6+\frac {32}{7} (x+1)^5+\frac {40}{7} (x+1)^4+\frac {32}{5} (x+1)^3+6 (x+1)^2+4 (x+1)+1\right ) \]