Internal problem ID [13614]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises.
page 641
Problem number: 33.5 (L).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime } x -2 y x=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
Order:=6; dsolve(diff(y(x),x$2)-x*diff(y(x),x)-2*x*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+\frac {1}{3} x^{3}+\frac {1}{20} x^{5}\right ) y \left (0\right )+\left (x +\frac {1}{6} x^{3}+\frac {1}{6} x^{4}+\frac {1}{40} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 49
AsymptoticDSolveValue[y''[x]-x*y'[x]-2*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^5}{20}+\frac {x^3}{3}+1\right )+c_2 \left (\frac {x^5}{40}+\frac {x^4}{6}+\frac {x^3}{6}+x\right ) \]