32.3.13 problem Exact Differential equations. Exercise 9.17, page 79

Internal problem ID [5811]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 9
Problem number : Exact Differential equations. Exercise 9.17, page 79
Date solved : Sunday, March 30, 2025 at 10:18:32 AM
CAS classification : [_exact]

\begin{align*} y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.110 (sec). Leaf size: 23

ode:=y(x)^2*exp(x*y(x)^2)+4*x^3+(2*x*y(x)*exp(x*y(x)^2)-3*y(x)^2)*diff(y(x),x) = 0; 
ic:=y(1) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (-{\mathrm e}^{x \,\textit {\_Z}^{2}}-x^{4}+\textit {\_Z}^{3}+2\right ) \]

✓ Mathematica. Time used: 0.386 (sec). Leaf size: 23

ode=(y[x]^2*Exp[x*y[x]^2]+4*x^3)+(2*x*y[x]*Exp[x*y[x]^2]-3*y[x]^2)*D[y[x],x]==0; 
ic=y[1]==0; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x^4+e^{x y(x)^2}-y(x)^3=2,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**3 + (2*x*y(x)*exp(x*y(x)**2) - 3*y(x)**2)*Derivative(y(x), x) + y(x)**2*exp(x*y(x)**2),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out