Internal problem ID [12172]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}=-1} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 33
dsolve((1+x^2)*diff(y(x),x$2)+diff(y(x),x)^2+1=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\ln \left (c_{1} x -1\right ) c_{1}^{2}+c_{2} c_{1}^{2}+c_{1} x +\ln \left (c_{1} x -1\right )}{c_{1}^{2}} \]
✓ Solution by Mathematica
Time used: 12.07 (sec). Leaf size: 33
DSolve[(1+x^2)*y''[x]+y'[x]^2+1==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x \cot (c_1)+\csc ^2(c_1) \log (-x \sin (c_1)-\cos (c_1))+c_2 \]