51.1.42 problem 42

Internal problem ID [10312]
Book : First order enumerated odes
Section : section 1
Problem number : 42
Date solved : Tuesday, September 30, 2025 at 07:19:18 PM
CAS classification : [_quadrature]

\begin{align*} x y \sin \left (x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 9

ode:=x*y(x)*sin(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 12

ode=x*y[x]*Sin[x]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 0\\ y(x)&\to c_1 \end{align*}

✓ Sympy. Time used: 0.085 (sec). Leaf size: 3

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

\[ y{\left (x \right )} = C_{1} \]