57.1.45 problem 45

Internal problem ID [9029]
Book : First order enumerated odes
Section : section 1
Problem number : 45
Date solved : Sunday, March 30, 2025 at 01:59:36 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.046 (sec). Leaf size: 5

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

\[ y = c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 7

ode=x*Sin[x]*D[y[x],x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 \]

✓ Sympy. Time used: 0.036 (sec). Leaf size: 3

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

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