Internal problem ID [11748]
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 (ix).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z=0} \] With initial conditions \begin {align*} [z \left (1\right ) = 2, z^{\prime }\left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve([3*x^2*diff(z(x),x$2)+5*x*diff(z(x),x)-z(x)=0,z(1) = 2, D(z)(1) = -1],z(x), singsol=all)
\[ z \left (x \right ) = \frac {3 x^{\frac {4}{3}}+5}{4 x} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 21
DSolve[{3*x^2*z''[x]+5*x*z'[x]-z[x]==0,{z[1]==2,z'[1]==-1}},z[x],x,IncludeSingularSolutions -> True]
\[ z(x)\to \frac {3 x^{4/3}+5}{4 x} \]