Internal problem ID [10832]
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 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }+{y^{\prime }}^{2}-1=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 5
dsolve([diff(y(x),x$2)+diff(y(x),x)^2=1,y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 6
DSolve[{y''[x]+y'[x]^2==1,{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \\ \end{align*}