Internal problem ID [12137]
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.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{3}-y^{\prime } {\mathrm e}^{2 x}=0} \]
✓ Solution by Maple
Time used: 0.062 (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 \left (x \right ) &= -{\mathrm e}^{x}+c_{1} \\ y \left (x \right ) &= {\mathrm e}^{x}+c_{1} \\ y \left (x \right ) &= c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 29
DSolve[y'[x]^3-y'[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*}