85.15.8 problem 1 (h)

Internal problem ID [22533]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 47
Problem number : 1 (h)
Date solved : Thursday, October 02, 2025 at 08:48:29 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 55

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

\begin{align*} y &= -\frac {\ln \left (x \right )}{2}-\frac {\sqrt {9 \ln \left (x \right )^{2}-12 x^{3}-36 c_1}}{6} \\ y &= -\frac {\ln \left (x \right )}{2}+\frac {\sqrt {9 \ln \left (x \right )^{2}-12 x^{3}-36 c_1}}{6} \\ \end{align*}

✓ Mathematica. Time used: 0.361 (sec). Leaf size: 98

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

\begin{align*} y(x)&\to \frac {1}{6} \left (-3 \log (x)-\sqrt {3} \sqrt {\frac {1}{x}} \sqrt {-4 x^4+3 x \log ^2(x)+12 c_1 x}\right )\\ y(x)&\to \frac {1}{6} \left (-3 \log (x)+\sqrt {3} \sqrt {\frac {1}{x}} \sqrt {-4 x^4+3 x \log ^2(x)+12 c_1 x}\right ) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**3 - y(x))/(x*(2*y(x) + log(x))) canno