Internal problem ID [13942]
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: 33.11 (f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime } \sin \left (x \right )-y x=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
Order:=5; dsolve(diff(y(x),x$2)-sin(x)*diff(y(x),x)-x*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+\frac {x^{3}}{6}\right ) y \left (0\right )+\left (x +\frac {1}{6} x^{3}+\frac {1}{12} x^{4}\right ) D\left (y \right )\left (0\right )+O\left (x^{5}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 35
AsymptoticDSolveValue[y''[x]-Sin[x]*y'[x]-x*y[x]==0,y[x],{x,0,4}]
\[ y(x)\to c_1 \left (\frac {x^3}{6}+1\right )+c_2 \left (\frac {x^4}{12}+\frac {x^3}{6}+x\right ) \]