Internal problem ID [5858]
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: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 52
Order:=8; dsolve(diff(y(x),x$2)+3/x*diff(y(x),x)-2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} \left (1+\frac {1}{4} x^{2}+\frac {1}{48} x^{4}+\frac {1}{1152} x^{6}+\mathrm {O}\left (x^{8}\right )\right ) x^{2}+c_{2} \left (\ln \relax (x ) \left (\left (-2\right ) x^{2}-\frac {1}{2} x^{4}-\frac {1}{24} x^{6}+\mathrm {O}\left (x^{8}\right )\right )+\left (-2+\frac {3}{8} x^{4}+\frac {7}{144} x^{6}+\mathrm {O}\left (x^{8}\right )\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 74
AsymptoticDSolveValue[y''[x]+3/x*y'[x]-2*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (\frac {x^6}{1152}+\frac {x^4}{48}+\frac {x^2}{4}+1\right )+c_1 \left (\frac {1}{48} \left (x^4+12 x^2+48\right ) \log (x)-\frac {5 x^6+45 x^4+72 x^2-144}{144 x^2}\right ) \]