73.23.31 problem 33.11 (e)

Internal problem ID [15677]
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 (e)
Date solved : Tuesday, January 28, 2025 at 08:04:03 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y x&=\sin \left (x \right ) \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 34

Order:=5; 
dsolve(diff(y(x),x$2)+x*y(x)=sin(x),y(x),type='series',x=0);
 

\[ y = \left (1-\frac {x^{3}}{6}\right ) y \left (0\right )+\left (x -\frac {1}{12} x^{4}\right ) y^{\prime }\left (0\right )+\frac {x^{3}}{6}+O\left (x^{5}\right ) \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 35

AsymptoticDSolveValue[D[y[x],{x,2}]+x*y[x]==Sin[x],y[x],{x,0,"5"-1}]
 

\[ y(x)\to c_2 \left (x-\frac {x^4}{12}\right )+\frac {x^3}{6}+c_1 \left (1-\frac {x^3}{6}\right ) \]