62.16.4 problem Ex 4

Internal problem ID [12895]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 27. Clairaut equation. Page 56
Problem number : Ex 4
Date solved : Tuesday, January 28, 2025 at 04:32:22 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} {\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x}&=0 \end{align*}

✓ Solution by Maple

Time used: 2.986 (sec). Leaf size: 24

dsolve(exp(2*y(x))*diff(y(x),x)^3+(exp(2*x)+exp(3*x))*diff(y(x),x)-exp(3*x)=0,y(x), singsol=all)
 

\[ y = \frac {\ln \left (-\left (c_{1} +1\right ) \left (c_{1} {\mathrm e}^{-x}-1\right )^{2}\right )}{2}+x \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[Exp[2*y[x]]*(D[y[x],x])^3+(Exp[2*x]+Exp[3*x])*D[y[x],x]-Exp[3*x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out