75.3.21 problem 21

Internal problem ID [19925]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 21
Date solved : Thursday, October 02, 2025 at 05:01:34 PM
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: 0.055 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.167 (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]
 

\begin{align*} y(x)&\to e^{-\frac {x^2}{3}+\frac {c_1}{x}} \end{align*}

✓ Sympy. Time used: 0.531 (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)
 

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