Internal problem ID [11888]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 6, Series solutions of linear differential equations. Section 6.1. Exercises page
232
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime } x +\left (3 x +2\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
Order:=6; dsolve(diff(y(x),x$2)+x*diff(y(x),x)+(3*x+2)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-x^{2}-\frac {1}{2} x^{3}+\frac {1}{3} x^{4}+\frac {11}{40} x^{5}\right ) y \left (0\right )+\left (x -\frac {1}{2} x^{3}-\frac {1}{4} x^{4}+\frac {1}{8} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 61
AsymptoticDSolveValue[y''[x]+x*y'[x]+(3*x+2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{8}-\frac {x^4}{4}-\frac {x^3}{2}+x\right )+c_1 \left (\frac {11 x^5}{40}+\frac {x^4}{3}-\frac {x^3}{2}-x^2+1\right ) \]