Internal problem ID [15101]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8. First order not solved for the derivative. Exercises page 67
Problem number: 213.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y-\left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(y(x)=(diff(y(x),x)-1)*exp(diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -1 \\ y \left (x \right ) &= \left (\ln \left (x -c_{1} \right )-1\right ) \left (x -c_{1} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.435 (sec). Leaf size: 22
DSolve[y[x]==(y'[x]-1)*Exp[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x+c_1) (-1+\log (x+c_1)) \\ y(x)\to -1 \\ \end{align*}