69.12.32 problem 306

Internal problem ID [18185]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 306
Date solved : Thursday, October 02, 2025 at 03:08:14 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.054 (sec). Leaf size: 32

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

\[ c_1 -\cos \left (\ln \left (x \right )\right ) x +\sin \left (\ln \left (x \right )\right ) x -\cos \left (\ln \left (y\right )\right ) y-\sin \left (\ln \left (y\right )\right ) y = 0 \]

✓ Mathematica. Time used: 0.189 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\cos (\log (K[1]))dK[1]\&\right ]\left [\int _1^x\sin (\log (K[2]))dK[2]+c_1\right ] \end{align*}

✗ Sympy

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

Timed Out