Internal problem ID [5835]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.034 (sec). Leaf size: 72
Order:=8; dsolve((x^3+4*x)*diff(y(x),x$2)-2*x*diff(y(x),x)+6*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \ln \relax (x ) \left (-\frac {3}{2} x +\frac {3}{4} x^{2}-\frac {1}{16} x^{3}-\frac {1}{32} x^{4}+\frac {1}{256} x^{5}+\frac {5}{1536} x^{6}-\frac {5}{14336} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) c_{2}+c_{1} x \left (1-\frac {1}{2} x +\frac {1}{24} x^{2}+\frac {1}{48} x^{3}-\frac {1}{384} x^{4}-\frac {5}{2304} x^{5}+\frac {5}{21504} x^{6}+\frac {15}{50176} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+\left (1+\frac {1}{2} x -\frac {7}{4} x^{2}+\frac {31}{96} x^{3}+\frac {1}{24} x^{4}-\frac {67}{3072} x^{5}-\frac {43}{10240} x^{6}+\frac {43061}{18063360} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.229 (sec). Leaf size: 121
AsymptoticDSolveValue[(x^3+4*x)*y''[x]-2*x*y'[x]+6*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {x \left (5 x^5+6 x^4-48 x^3-96 x^2+1152 x-2304\right ) \log (x)}{1536}+\frac {-229 x^6-790 x^5+2240 x^4+11840 x^3-76800 x^2+61440 x+30720}{30720}\right )+c_2 \left (\frac {5 x^7}{21504}-\frac {5 x^6}{2304}-\frac {x^5}{384}+\frac {x^4}{48}+\frac {x^3}{24}-\frac {x^2}{2}+x\right ) \]