Internal problem ID [6462]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+\left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 14
dsolve((1+x^2)*diff(y(x),x$2)+diff(y(x),x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = \int \frac {1}{\arctan \relax (x )+c_{1}}d x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 25
DSolve[(1+x^2)*y''[x]+(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \int _1^x\frac {1}{\text {ArcTan}(K[1])-c_1}dK[1]+c_2 \\ \end{align*}