Internal problem ID [5720]
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(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 3\).
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 54
Order:=8; dsolve((x^2-x-6)*diff(y(x),x$2)+(5+3*x)*diff(y(x),x)+y(x)=0,y(x),type='series',x=3);
\[ y \relax (x ) = \frac {c_{2} \left (1-\frac {1}{14} \left (x -3\right )+\frac {1}{133} \left (x -3\right )^{2}-\frac {1}{1064} \left (x -3\right )^{3}+\frac {1}{7714} \left (x -3\right )^{4}-\frac {5}{262276} \left (x -3\right )^{5}+\frac {5}{1704794} \left (x -3\right )^{6}-\frac {5}{10715848} \left (x -3\right )^{7}+\mathrm {O}\left (\left (x -3\right )^{8}\right )\right ) \left (x -3\right )^{\frac {9}{5}}+c_{1} \left (1+\frac {4}{25} \left (x -3\right )-\frac {2}{625} \left (x -3\right )^{2}+\frac {4}{15625} \left (x -3\right )^{3}-\frac {11}{390625} \left (x -3\right )^{4}+\frac {176}{48828125} \left (x -3\right )^{5}-\frac {616}{1220703125} \left (x -3\right )^{6}+\frac {2288}{30517578125} \left (x -3\right )^{7}+\mathrm {O}\left (\left (x -3\right )^{8}\right )\right )}{\left (x -3\right )^{\frac {9}{5}}} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 145
AsymptoticDSolveValue[(x^2-x-6)*y''[x]+(5+3*x)*y'[x]+y[x]==0,y[x],{x,3,7}]
\[ y(x)\to c_1 \left (-\frac {5 (x-3)^7}{10715848}+\frac {5 (x-3)^6}{1704794}-\frac {5 (x-3)^5}{262276}+\frac {(x-3)^4}{7714}-\frac {(x-3)^3}{1064}+\frac {1}{133} (x-3)^2+\frac {3-x}{14}+1\right )+\frac {c_2 \left (\frac {2288 (x-3)^7}{30517578125}-\frac {616 (x-3)^6}{1220703125}+\frac {176 (x-3)^5}{48828125}-\frac {11 (x-3)^4}{390625}+\frac {4 (x-3)^3}{15625}-\frac {2}{625} (x-3)^2+\frac {4 (x-3)}{25}+1\right )}{(x-3)^{9/5}} \]