83.3.14 problem 14

Internal problem ID [18991]
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, March 13, 2025 at 01:18:11 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: 0.049 (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);
 

\[ \ln \left (x \right ) x^{2}-y \left (x \right ) \sin \left (y \left (x \right )\right )+c_{1} = 0 \]

✓ Mathematica. Time used: 0.518 (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]
 

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

✓ Sympy. Time used: 2.198 (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)
 

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