29.4.4 problem 4

Internal problem ID [7257]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 04:26:25 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 22

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

\[ x^{2} {\mathrm e}^{3 y}+{\mathrm e}^{x}-\frac {y^{3}}{3}+c_1 = 0 \]

✓ Mathematica. Time used: 0.17 (sec). Leaf size: 28

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

\[ \text {Solve}\left [x^2 e^{3 y(x)}-\frac {1}{3} y(x)^3+e^x=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out