Internal problem ID [5837]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.3 SOLUTIONS ABOUT
SINGULAR POINTS. EXERCISES 6.3. Page 255
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (x -2\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 74
Order:=8; dsolve((x^2+x-6)*diff(y(x),x$2)+(x+3)*diff(y(x),x)+(x-2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {1}{6} x^{2}-\frac {1}{108} x^{3}-\frac {17}{2592} x^{4}-\frac {7}{2160} x^{5}-\frac {139}{116640} x^{6}-\frac {5377}{9797760} x^{7}\right ) y \relax (0)+\left (x +\frac {1}{4} x^{2}+\frac {1}{36} x^{3}+\frac {23}{864} x^{4}+\frac {13}{1440} x^{5}+\frac {619}{155520} x^{6}+\frac {689}{408240} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 98
AsymptoticDSolveValue[(x^2+x-6)*y''[x]+(x+3)*y'[x]+(x-2)*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (-\frac {5377 x^7}{9797760}-\frac {139 x^6}{116640}-\frac {7 x^5}{2160}-\frac {17 x^4}{2592}-\frac {x^3}{108}-\frac {x^2}{6}+1\right )+c_2 \left (\frac {689 x^7}{408240}+\frac {619 x^6}{155520}+\frac {13 x^5}{1440}+\frac {23 x^4}{864}+\frac {x^3}{36}+\frac {x^2}{4}+x\right ) \]