Internal problem ID [11745]
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]]
\[ \boxed {x^{2} y^{\prime \prime }-x y^{\prime }-3 y=0} \] 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: 0.138 (sec). Leaf size: 169
DSolve[{x^2*y''[x]-x*y[x]-3*y[x]==0,{y[1]==1,y'[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt {x} \left (\left (3 \operatorname {BesselI}\left (-\sqrt {13},2\right )+\operatorname {BesselI}\left (-1-\sqrt {13},2\right )+\operatorname {BesselI}\left (1-\sqrt {13},2\right )\right ) \operatorname {BesselI}\left (\sqrt {13},2 \sqrt {x}\right )-\left (3 \operatorname {BesselI}\left (\sqrt {13},2\right )+\operatorname {BesselI}\left (-1+\sqrt {13},2\right )+\operatorname {BesselI}\left (1+\sqrt {13},2\right )\right ) \operatorname {BesselI}\left (-\sqrt {13},2 \sqrt {x}\right )\right )}{\operatorname {BesselI}\left (\sqrt {13},2\right ) \left (\operatorname {BesselI}\left (-1-\sqrt {13},2\right )+\operatorname {BesselI}\left (1-\sqrt {13},2\right )\right )-\operatorname {BesselI}\left (-\sqrt {13},2\right ) \left (\operatorname {BesselI}\left (-1+\sqrt {13},2\right )+\operatorname {BesselI}\left (1+\sqrt {13},2\right )\right )} \]