Internal problem ID [8715]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1135.
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 {4 x y^{\prime \prime }+2 y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(4*x*diff(diff(y(x),x),x)+2*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sinh \left (\sqrt {x}\right )+c_{2} \cosh \left (\sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 27
DSolve[-y[x] + 2*y'[x] + 4*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cosh \left (\sqrt {x}\right )+i c_2 \sinh \left (\sqrt {x}\right ) \\ \end{align*}