Internal problem ID [12756]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {y^{\prime \prime } x^{2}-y^{\prime } x +y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 2, y^{\prime }\left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 12
dsolve([x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(1) = 2, D(y)(1) = -1],y(x), singsol=all)
\[ y \left (x \right ) = x \left (2-3 \ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 13
DSolve[{x^2*y''[x]-x*y'[x]+y[x]==0,{y[1]==2,y'[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (2-3 \log (x)) \]