58.1.17 problem 17

Internal problem ID [9088]
Book : Second order enumerated odes
Section : section 1
Problem number : 17
Date solved : Monday, January 27, 2025 at 05:37:05 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)+diff(y(x),x)^2=1,y(x), singsol=all)
 

\[ y = x -\ln \left (2\right )+\ln \left (c_{1} {\mathrm e}^{-2 x}-c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.354 (sec). Leaf size: 48

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

\begin{align*} y(x)\to -\frac {1}{2} \log \left (e^{2 x}\right )+\log \left (e^{2 x}+e^{2 c_1}\right )+c_2 \\ y(x)\to \frac {1}{2} \log \left (e^{2 x}\right )+c_2 \\ \end{align*}