Internal problem ID [2396]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 41, page 195
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (8-x \right ) x^{2} y^{\prime \prime }+6 y^{\prime } x -y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
Order:=6; dsolve((8-x)*x^2*diff(y(x),x$2)+6*x*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{2} x^{\frac {3}{4}} \left (1-\frac {1}{56} x -\frac {3}{9856} x^{2}-\frac {1}{78848} x^{3}-\frac {5}{6848512} x^{4}-\frac {63}{1260126208} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{1} \left (1+\frac {5}{32} x -\frac {3}{2048} x^{2}-\frac {7}{196608} x^{3}-\frac {539}{327155712} x^{4}-\frac {5929}{59324235776} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x^{\frac {1}{4}}} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 90
AsymptoticDSolveValue[(8-x)*x^2*y''[x]+6*x*y'[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt {x} \left (-\frac {63 x^5}{1260126208}-\frac {5 x^4}{6848512}-\frac {x^3}{78848}-\frac {3 x^2}{9856}-\frac {x}{56}+1\right )+\frac {c_2 \left (-\frac {5929 x^5}{59324235776}-\frac {539 x^4}{327155712}-\frac {7 x^3}{196608}-\frac {3 x^2}{2048}+\frac {5 x}{32}+1\right )}{\sqrt [4]{x}} \]