83.4.8 problem 2 (c)

Internal problem ID [21935]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. V at page 42
Problem number : 2 (c)
Date solved : Thursday, October 02, 2025 at 08:16:34 PM
CAS classification : [_exact]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.132 (sec). Leaf size: 26

ode:=y(x)*exp(2*x)-3*x*exp(2*y(x))+(1/2*exp(2*x)-3*x^2*exp(2*y(x))-exp(y(x)))*diff(y(x),x) = 0; 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (-3 x^{2} {\mathrm e}^{2 \textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{2 x}-2 \,{\mathrm e}^{\textit {\_Z}}+5\right ) \]

✓ Mathematica. Time used: 0.242 (sec). Leaf size: 31

ode=(y[x]*Exp[2*x]-3*x*Exp[2*y[x]] )+(1/2*Exp[2*x]-3*x^2*Exp[2*y[x]]-Exp[y[x]] )*D[y[x],x]==0; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [-3 x^2 e^{2 y(x)}-2 e^{y(x)}+e^{2 x} y(x)=-5,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x*exp(2*y(x)) + (-3*x**2*exp(2*y(x)) + exp(2*x)/2 - exp(y(x)))*Derivative(y(x), x) + y(x)*exp(2*x),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out