15.8.40 problem 42

Internal problem ID [3043]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 42
Date solved : Sunday, March 30, 2025 at 01:13:30 AM
CAS classification : [_exact]

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

With initial conditions

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

✓ Maple. Time used: 0.387 (sec). Leaf size: 40

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

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

✓ Mathematica. Time used: 0.774 (sec). Leaf size: 30

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

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

✗ Sympy

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

Timed Out