Internal problem ID [4156]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 8. Special second order equations. Lesson 35. Independent variable x
absent
Problem number: Exercise 35.14, page 504.
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}+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 27
dsolve((1+x^2)*diff(y(x),x$2)+(diff(y(x),x))^2+1=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{c_{1}}+\ln \left (c_{1} x -1\right )+\frac {\ln \left (c_{1} x -1\right )}{c_{1}^{2}}+c_{2} \]
✓ Solution by Mathematica
Time used: 7.039 (sec). Leaf size: 33
DSolve[(1+x^2)*y''[x]+(y'[x])^2+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \cot (c_1)+\csc ^2(c_1) \log (-x \sin (c_1)-\cos (c_1))+c_2 \\ \end{align*}