75.8.15 problem 213

Internal problem ID [16831]
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
Date solved : Tuesday, January 28, 2025 at 09:34:16 AM
CAS classification : [_quadrature]

\begin{align*} y&=\left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \end{align*}

✓ Solution by Maple

Time used: 0.133 (sec). Leaf size: 22

dsolve(y(x)=(diff(y(x),x)-1)*exp(diff(y(x),x)),y(x), singsol=all)
 

\begin{align*} y &= -1 \\ y &= \left (\ln \left (x -c_{1} \right )-1\right ) \left (x -c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.218 (sec). Leaf size: 35

DSolve[y[x]==(D[y[x],x]-1)*Exp[D[y[x],x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{W\left (\frac {K[1]}{e}\right )+1}dK[1]\&\right ][x+c_1] \\ y(x)\to -1 \\ \end{align*}