Internal problem ID [12067]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 19, CauchyEuler equations. Exercises page 174
Problem number: 19.1 (viii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = -2, y^{\prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve([x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+5*y(x)=0,y(1) = -2, D(y)(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {3}{4} x^{5}-\frac {11}{4} x \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 17
DSolve[{x^2*y''[x]-5*x*y'[x]+5*y[x]==0,{y[1]==-2,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} x \left (3 x^4-11\right ) \]