Internal problem ID [11876]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = -5] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+3*y(x)=0,y(1) = 1, D(y)(1) = -5],y(x), singsol=all)
\[ y \left (x \right ) = \frac {-x^{2}+2}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 16
DSolve[{x^2*y''[x]+5*x*y'[x]+3*y[x]==0,{y[1]==1,y'[1]==-5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2-x^2}{x^3} \]