66.2.17 problem Problem 17

Internal problem ID [13916]
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
Date solved : Tuesday, January 28, 2025 at 06:08:26 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.069 (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)
 

\[ y = x \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 6

DSolve[{D[y[x],{x,2}]+D[y[x],x]^2==1,{y[0]==0,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \]