Internal problem ID [11896]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 6, Series solutions of linear differential equations. Section 6.1. Exercises page
232
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y x=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 3] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
Order:=6; dsolve([(x^2+1)*diff(y(x),x$2)+x*diff(y(x),x)+2*x*y(x)=0,y(0) = 2, D(y)(0) = 3],y(x),type='series',x=0);
\[ y \left (x \right ) = 2+3 x -\frac {7}{6} x^{3}-\frac {1}{2} x^{4}+\frac {21}{40} x^{5}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 29
AsymptoticDSolveValue[{(x^2+1)*y''[x]+x*y'[x]+2*x*y[x]==0,{y[0]==2,y'[0]==3}},y[x],{x,0,5}]
\[ y(x)\to \frac {21 x^5}{40}-\frac {x^4}{2}-\frac {7 x^3}{6}+3 x+2 \]