Internal problem ID [15479]
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: 735.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-\left (x^{2}+1\right ) y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -2, y^{\prime }\left (0\right ) = 2] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=6; dsolve([diff(y(x),x$2)-(1+x^2)*y(x)=0,y(0) = -2, D(y)(0) = 2],y(x),type='series',x=0);
\[ y = -2+2 x -x^{2}+\frac {1}{3} x^{3}-\frac {1}{4} x^{4}+\frac {7}{60} x^{5}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 34
AsymptoticDSolveValue[{y''[x]-(1+x^2)*y[x]==0,{y[0]==-2,y'[0]==2}},y[x],{x,0,5}]
\[ y(x)\to \frac {7 x^5}{60}-\frac {x^4}{4}+\frac {x^3}{3}-x^2+2 x-2 \]