Internal problem ID [13665]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 20. Euler equations. Additional exercises page 382
Problem number: 20.2 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +2 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 3, y^{\prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 17
dsolve([x^2*diff(y(x),x$2)-x*diff(y(x),x)+2*y(x)=0,y(1) = 3, D(y)(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \left (-3 \sin \left (\ln \left (x \right )\right )+3 \cos \left (\ln \left (x \right )\right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 17
DSolve[{x^2*y''[x]-x*y'[x]+2*y[x]==0,{y[1]==3,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 x (\cos (\log (x))-\sin (\log (x))) \]