Internal problem ID [13246]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 15. General solutions to Homogeneous linear differential equations. Additional
exercises page 294
Problem number: 15.2 (g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 5, y^{\prime }\left (1\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(1) = 5, D(y)(1) = 3],y(x), singsol=all)
\[ y = x \left (5-2 \ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 13
DSolve[{x^2*y''[x]-x*y'[x]+y[x]==0,{y[1]==5,y'[1]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (5-2 \log (x)) \]