54.1.355 problem 362

Internal problem ID [11669]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 362
Date solved : Tuesday, September 30, 2025 at 10:05:15 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} \left (x^{2} y \sin \left (x y\right )-4 x \right ) y^{\prime }+x y^{2} \sin \left (x y\right )-y&=0 \end{align*}

✓ Maple. Time used: 0.067 (sec). Leaf size: 22

ode:=(x^2*y(x)*sin(x*y(x))-4*x)*diff(y(x),x)+x*y(x)^2*sin(x*y(x))-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (\textit {\_Z} -{\mathrm e}^{-\frac {\cos \left (\textit {\_Z} \right )}{4}} c_1 \,x^{{3}/{4}}\right )}{x} \]

✓ Mathematica. Time used: 0.169 (sec). Leaf size: 23

ode=-y[x] + x*Sin[x*y[x]]*y[x]^2 + (-4*x + x^2*Sin[x*y[x]]*y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}[-4 \log (y(x))-\cos (x y(x))-\log (x)=c_1,y(x)] \]

✓ Sympy. Time used: 1.151 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x)**2*sin(x*y(x)) + (x**2*y(x)*sin(x*y(x)) - 4*x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ - \log {\left (x \right )} + \frac {4 \log {\left (x y{\left (x \right )} \right )}}{3} + \frac {\cos {\left (x y{\left (x \right )} \right )}}{3} = C_{1} \]