66.1.26 problem Problem 37

Internal problem ID [13802]
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 : Monday, March 31, 2025 at 08:12:59 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.032 (sec). Leaf size: 21

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

\begin{align*} y &= -{\mathrm e}^{x}+c_1 \\ y &= {\mathrm e}^{x}+c_1 \\ y &= c_1 \\ \end{align*}

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

ode=D[y[x],x]^3-D[y[x],x]*Exp[2*x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.168 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(2*x)*Derivative(y(x), x) + Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} + e^{x}, \ y{\left (x \right )} = C_{1} - e^{x}, \ y{\left (x \right )} = C_{1}\right ] \]