Internal problem ID [5058]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 2. Linear homogeneous equations. Section 2.2 problems. page 95
Problem number: 51.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((x^2+1)*diff(y(x),x$2)+x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sin \left (\operatorname {arcsinh}\left (x \right )\right )+c_{2} \cos \left (\operatorname {arcsinh}\left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 18
DSolve[(x^2+1)*y''[x]+x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos (\text {arcsinh}(x))+c_2 \sin (\text {arcsinh}(x)) \\ \end{align*}