Internal problem ID [10717]
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 (vi).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x -3 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 7
dsolve([x^2*diff(y(x),x$2)-x*diff(y(x),x)-3*y(x)=0,y(1) = 1, D(y)(1) = -1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{x} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 151
DSolve[{x^2*y''[x]-x*y[x]-3*y[x]==0,{y[1]==1,y'[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {x} \left (\left (\left (\sqrt {13}-3\right ) \operatorname {BesselI}\left (\sqrt {13},2\right )-2 \, _0\tilde {F}_1\left (;\sqrt {13};1\right )\right ) \operatorname {BesselI}\left (-\sqrt {13},2 \sqrt {x}\right )+\left (2 \, _0\tilde {F}_1\left (;-\sqrt {13};1\right )+\left (3+\sqrt {13}\right ) \operatorname {BesselI}\left (-\sqrt {13},2\right )\right ) \operatorname {BesselI}\left (\sqrt {13},2 \sqrt {x}\right )\right )}{2 \, _0\tilde {F}_1\left (;-\sqrt {13};1\right ) \operatorname {BesselI}\left (\sqrt {13},2\right )+\operatorname {BesselI}\left (-\sqrt {13},2\right ) \left (2 \sqrt {13} \operatorname {BesselI}\left (\sqrt {13},2\right )-2 \, _0\tilde {F}_1\left (;\sqrt {13};1\right )\right )} \\ \end{align*}