Internal problem ID [3826]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1141.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {{\mathrm e}^{y^{\prime }-y}-\left (y^{\prime }\right )^{2}+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve(exp(diff(y(x),x)-y(x))-diff(y(x),x)^2+1 = 0,y(x), singsol=all)
\[ x -\left (\int _{}^{y \relax (x )}\frac {1}{\RootOf \left (-{\mathrm e}^{-\textit {\_a} +\textit {\_Z}}+\textit {\_Z}^{2}-1\right )}d \textit {\_a} \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.135 (sec). Leaf size: 44
DSolve[Exp[y'[x]-y[x]]-(y'[x])^2+1==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=-\log (1-K[1])+\log (K[1])+\log (K[1]+1)+c_1,y(x)=K[1]-\log \left (K[1]^2-1\right )\right \},\{y(x),K[1]\}\right ] \]