75.23.11 problem 734

Internal problem ID [17208]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 18.1 Integration of differential equation in series. Power series. Exercises page 171
Problem number : 734
Date solved : Tuesday, January 28, 2025 at 09:57:40 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-x y^{\prime }+y&=1 \end{align*}

Using series method with expansion around

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 12

Order:=6; 
dsolve([diff(y(x),x$2)-x*diff(y(x),x)+y(x)=1,y(0) = 0, D(y)(0) = 0],y(x),type='series',x=0);
 

\[ y = \frac {1}{2} x^{2}+\frac {1}{24} x^{4}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 18

AsymptoticDSolveValue[{D[y[x],{x,2}]-x*D[y[x],x]+y[x]==1,{y[0]==0,Derivative[1][y][0] ==0}},y[x],{x,0,"6"-1}]
 

\[ y(x)\to \frac {x^4}{24}+\frac {x^2}{2} \]