77.8.21 problem 22

Internal problem ID [20432]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 22
Date solved : Thursday, October 02, 2025 at 05:59:37 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x \left (2 \ln \left (x \right )+1\right )}{\sin \left (y\right )+y \cos \left (y\right )} \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 18

ode:=diff(y(x),x) = x*(2*ln(x)+1)/(sin(y(x))+y(x)*cos(y(x))); 
dsolve(ode,y(x), singsol=all);
 

\[ x^{2} \ln \left (x \right )-y \sin \left (y\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.334 (sec). Leaf size: 22

ode=D[y[x],x]==(x*(2*Log[x]+1))/(Sin[y[x]]+y[x]*Cos[y[x]]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.725 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(2*log(x) + 1)/(y(x)*cos(y(x)) + sin(y(x))) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} \sin {\left (y{\left (x \right )} \right )} = C_{1} + x^{2} \log {\left (x \right )} \]