Internal problem ID [5466]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 26. Integration in series (singular points). Supplemetary problems. Page
218
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
Order:=6; dsolve(x^2*(x+1)*diff(y(x),x$2)+x*(x+1)*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x \left (1-\frac {1}{3} x +\frac {1}{6} x^{2}-\frac {1}{10} x^{3}+\frac {1}{15} x^{4}-\frac {1}{21} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-2-2 x +\operatorname {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 45
AsymptoticDSolveValue[x^2*(x+1)*y''[x]+x*(x+1)*y'[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{15}-\frac {x^4}{10}+\frac {x^3}{6}-\frac {x^2}{3}+x\right )+c_1 \left (\frac {1}{x}+1\right ) \]