Internal problem ID [11874]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 5, y^{\prime }\left (1\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([x^2*diff(y(x),x$2)-2*x*diff(y(x),x)-10*y(x)=0,y(1) = 5, D(y)(1) = 4],y(x), singsol=all)
\[ y \left (x \right ) = 2 x^{5}+\frac {3}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 16
DSolve[{x^2*y''[x]-2*x*y'[x]-10*y[x]==0,{y[1]==5,y'[1]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 x^7+3}{x^2} \]