Internal problem ID [2395]
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: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (4+x \right ) x^{2} y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
Order:=6; dsolve((4+x)*x^2*diff(y(x),x$2)+x*(x-1)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{\frac {1}{4}} \left (1-\frac {1}{16} x +\frac {5}{512} x^{2}-\frac {15}{8192} x^{3}+\frac {195}{524288} x^{4}-\frac {663}{8388608} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x \left (1-\frac {1}{7} x +\frac {2}{77} x^{2}-\frac {2}{385} x^{3}+\frac {8}{7315} x^{4}-\frac {8}{33649} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 86
AsymptoticDSolveValue[(4+x)*x^2*y''[x]+x*(x-1)*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 x \left (-\frac {8 x^5}{33649}+\frac {8 x^4}{7315}-\frac {2 x^3}{385}+\frac {2 x^2}{77}-\frac {x}{7}+1\right )+c_2 \sqrt [4]{x} \left (-\frac {663 x^5}{8388608}+\frac {195 x^4}{524288}-\frac {15 x^3}{8192}+\frac {5 x^2}{512}-\frac {x}{16}+1\right ) \]