Internal problem ID [11718]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page
113
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 3, y^{\prime }\left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve([x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,y(1) = 3, D(y)(1) = 2],y(x), singsol=all)
\[ y \left (x \right ) = -x^{2}+4 x \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 11
DSolve[{x^2*y''[x]-2*x*y'[x]+2*y[x]==0,{y[1]==3,y'[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -((x-4) x) \]