84.12.8 problem 6.13

Internal problem ID [22150]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 6. Exact first-order differential equations. Supplementary problems
Problem number : 6.13
Date solved : Thursday, October 02, 2025 at 08:32:32 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = \frac {c_1}{x \sin \left (x \right )+1} \]

✓ Mathematica. Time used: 0.129 (sec). Leaf size: 21

ode=(y[x]*Sin[x]+x*y[x]*Cos[x])+(x*Sin[x]+1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{x \sin (x)+1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.241 (sec). Leaf size: 10

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

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