77.3.14 problem 14

Internal problem ID [20355]
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. Exercise II (B) at page 9
Problem number : 14
Date solved : Thursday, October 02, 2025 at 05:46:25 PM
CAS classification : [_separable]

\begin{align*} \left (\sin \left (y\right )+y \cos \left (y\right )\right ) y^{\prime }-\left (2 \ln \left (x \right )+1\right ) x&=0 \end{align*}

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

ode:=(sin(y(x))+y(x)*cos(y(x)))*diff(y(x),x)-(2*ln(x)+1)*x = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.353 (sec). Leaf size: 22

ode=(Sin[y[x]]+y[x]*Cos[y[x]])*D[y[x],x]-(2*Log[x]+1)*x==0; 
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: 1.340 (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)
 

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