50.7.12 problem 3(b)

Internal problem ID [7916]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.9. Reduction of Order. Page 38
Problem number : 3(b)
Date solved : Monday, January 27, 2025 at 03:32:06 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: 0.009 (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: 0.436 (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*}