50.18.9 problem 4(a)

Internal problem ID [8103]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 4. Power Series Solutions and Special Functions. Section 4.3. Second-Order Linear Equations: Ordinary Points. Page 169
Problem number : 4(a)
Date solved : Monday, January 27, 2025 at 03:43:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime }-y x&=0 \end{align*}

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 20

Order:=8; 
dsolve([diff(y(x),x$2)+diff(y(x),x)-x*y(x)=0,y(0) = 1, D(y)(0) = 0],y(x),type='series',x=0);
 

\[ y = 1+\frac {1}{6} x^{3}-\frac {1}{24} x^{4}+\frac {1}{120} x^{5}+\frac {1}{240} x^{6}-\frac {1}{630} x^{7}+\operatorname {O}\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 40

AsymptoticDSolveValue[{D[y[x],{x,2}]+D[y[x],x]-x*y[x]==0,{y[0]==1,Derivative[1][y][0] ==0}},y[x],{x,0,"8"-1}]
 

\[ y(x)\to -\frac {x^7}{630}+\frac {x^6}{240}+\frac {x^5}{120}-\frac {x^4}{24}+\frac {x^3}{6}+1 \]