49.22.8 problem 1(h)

Internal problem ID [7754]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 198
Problem number : 1(h)
Date solved : Sunday, March 30, 2025 at 12:22:42 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=3*x^2*ln(x)+x^2+y(x)+x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-x^{3} \ln \left (x \right )+c_1}{x} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.195 (sec). Leaf size: 12

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

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