Internal problem ID [11741]
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 (ii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {4 x^{2} y^{\prime \prime }+y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 13
dsolve([4*x^2*diff(y(x),x$2)+y(x)=0,y(1) = 1, D(y)(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\sqrt {x}\, \left (-2+\ln \left (x \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 47
DSolve[{x^2*y''[x]+y[x]==0,{y[1]==1,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{3} \sqrt {x} \left (\sqrt {3} \sin \left (\frac {1}{2} \sqrt {3} \log (x)\right )-3 \cos \left (\frac {1}{2} \sqrt {3} \log (x)\right )\right ) \]