66.1.26 problem Problem 37

Internal problem ID [13873]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 37
Date solved : Tuesday, January 28, 2025 at 06:06:37 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3}-y^{\prime } {\mathrm e}^{2 x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.094 (sec). Leaf size: 21

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

\begin{align*} y &= -{\mathrm e}^{x}+c_{1} \\ y &= c_{1} +{\mathrm e}^{x} \\ y &= c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

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

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