Internal problem ID [4559]
Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.4, ODEs with variable Coefficients. Second
order and Homogeneous. page 318
Problem number: 10.4.8 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+\frac {y^{\prime }}{2}+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(x*diff(y(x),x$2)+1/2*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (2 \sqrt {2}\, \sqrt {x}\right )+c_{2} \cos \left (2 \sqrt {2}\, \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 38
DSolve[x*y''[x]+1/2*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos \left (2 \sqrt {2} \sqrt {x}\right )+c_2 \sin \left (2 \sqrt {2} \sqrt {x}\right ) \\ \end{align*}