28.1.24 problem 24

Internal problem ID [4330]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 24
Date solved : Sunday, March 30, 2025 at 03:01:39 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.119 (sec). Leaf size: 17

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

\[ y = {\mathrm e}^{-\frac {x^{2}}{3}-\frac {c_1}{x}} \]

✓ Mathematica. Time used: 0.244 (sec). Leaf size: 21

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

\[ y(x)\to e^{-\frac {x^2}{3}+\frac {c_1}{x}} \]

✓ Sympy. Time used: 0.891 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = e^{\frac {3 C_{1} - x^{3}}{3 x}} \]