15.21.7 problem 29

Internal problem ID [3331]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 39, page 179
Problem number : 29
Date solved : Monday, January 27, 2025 at 07:34:21 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y&=x y^{\prime }+{\mathrm e}^{y^{\prime }} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 26

DSolve[y[x]==D[y[x],x]*x+Exp[D[y[x],x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x+e^{c_1} \\ y(x)\to x (\log (-x)-1) \\ \end{align*}