73.7.44 problem 44

Internal problem ID [15131]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 44
Date solved : Monday, March 31, 2025 at 01:26:36 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 40

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

\begin{align*} y &= \frac {\sqrt {x \ln \left (x^{2}-c_1 \right )}}{x} \\ y &= -\frac {\sqrt {x \ln \left (x^{2}-c_1 \right )}}{x} \\ \end{align*}

✓ Mathematica. Time used: 1.259 (sec). Leaf size: 44

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

\begin{align*} y(x)\to -\frac {\sqrt {\log \left (x^2+c_1\right )}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {\log \left (x^2+c_1\right )}}{\sqrt {x}} \\ \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - exp(-x*y(x)**2)/y(x) + y(x)/(2*x) cannot be solved by the factorable group method