Internal problem ID [2391]
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: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+y \left (x -1\right )=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
Order:=6; dsolve(9*x^2*diff(y(x),x$2)+9*(x-x^2)*diff(y(x),x)+(x-1)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{2} x^{\frac {2}{3}} \left (1+\frac {2}{15} x +\frac {11}{360} x^{2}+\frac {1}{162} x^{3}+\frac {29}{27216} x^{4}+\frac {551}{3470040} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{1} \left (1-\frac {4}{3} x -\frac {5}{18} x^{2}-\frac {5}{81} x^{3}-\frac {23}{1944} x^{4}-\frac {92}{47385} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 90
AsymptoticDSolveValue[9*x^2*y''[x]+9*(x-x^2)*y'[x]+(x-1)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [3]{x} \left (\frac {551 x^5}{3470040}+\frac {29 x^4}{27216}+\frac {x^3}{162}+\frac {11 x^2}{360}+\frac {2 x}{15}+1\right )+\frac {c_2 \left (-\frac {92 x^5}{47385}-\frac {23 x^4}{1944}-\frac {5 x^3}{81}-\frac {5 x^2}{18}-\frac {4 x}{3}+1\right )}{\sqrt [3]{x}} \]