Internal problem ID [11719]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -4 y=0} \] With initial conditions \begin {align*} [y \left (2\right ) = 3, y^{\prime }\left (2\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=0,y(2) = 3, D(y)(2) = -1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{4}+32}{4 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 17
DSolve[{x^2*y''[x]+x*y'[x]-4*y[x]==0,{y[2]==3,y'[2]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^4+32}{4 x^2} \]