Internal problem ID [13662]
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 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y=0} \] With initial conditions \begin {align*} [y \left (4\right ) = 0, y^{\prime }\left (4\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([4*x^2*diff(y(x),x$2)+4*x*diff(y(x),x)-y(x)=0,y(4) = 0, D(y)(4) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {4 x -16}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 15
DSolve[{4*x^2*y''[x]+4*x*y'[x]-y[x]==0,{y[4]==0,y'[4]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {4 (x-4)}{\sqrt {x}} \]