12.6.15 problem 15

Internal problem ID [1694]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 15
Date solved : Saturday, March 29, 2025 at 11:33:26 PM
CAS classification : [_exact]

\begin{align*} x^{2} {\mathrm e}^{x^{2}+y} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{x^{2}+y}-12 y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 27

ode:=x^2*exp(y(x)+x^2)*(2*x^2+3)+4*x+(x^3*exp(y(x)+x^2)-12*y(x)^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ x^{3} {\mathrm e}^{x^{2}+y}-4 y^{3}+2 x^{2}+c_1 = 0 \]

✓ Mathematica. Time used: 0.484 (sec). Leaf size: 30

ode=(x^2*Exp[x^2+y[x]]*(2*x^2+3)+4*x)+(x^3*Exp[x^2+y[x]]-12*y[x]^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [2 x^2+x^3 e^{x^2+y(x)}-4 y(x)^3=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(2*x**2 + 3)*exp(x**2 + y(x)) + 4*x + (x**3*exp(x**2 + y(x)) - 12*y(x)**2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out