29.37.20 problem 1141

Internal problem ID [5678]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1141
Date solved : Monday, January 27, 2025 at 01:06:35 PM
CAS classification : [_quadrature]

\begin{align*} {\mathrm e}^{y^{\prime }-y}-{y^{\prime }}^{2}+1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 31

dsolve(exp(diff(y(x),x)-y(x))-diff(y(x),x)^2+1 = 0,y(x), singsol=all)
 

\[ x -\int _{}^{y \left (x \right )}\frac {1}{\operatorname {RootOf}\left (-{\mathrm e}^{-\textit {\_a} +\textit {\_Z}}+\textit {\_Z}^{2}-1\right )}d \textit {\_a} -c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 49

DSolve[Exp[D[y[x],x]-y[x]]-(D[y[x],x])^2+1==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\left \{x=\int \frac {1-\frac {2 K[1]}{K[1]^2-1}}{K[1]} \, dK[1]+c_1,y(x)=K[1]-\log \left (K[1]^2-1\right )\right \},\{y(x),K[1]\}\right ] \]