Internal problem ID [15478]
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 ODE’s). Section 18.1 Integration of differential equation in
series. Power series. Exercises page 171
Problem number: 734.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime } x +y=1} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (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: 0.013 (sec). Leaf size: 18
AsymptoticDSolveValue[{y''[x]-x*y'[x]+y[x]==1,{y[0]==0,y'[0]==0}},y[x],{x,0,5}]
\[ y(x)\to \frac {x^4}{24}+\frac {x^2}{2} \]