86.4.6 problem 6 (a)

Internal problem ID [23113]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 4. Linear equations of the first order. Exercise 4b at page 64
Problem number : 6 (a)
Date solved : Thursday, October 02, 2025 at 09:22:59 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = \left (\tan \left (x \right ) x +\ln \left (\cos \left (x \right )\right )+c_1 \right ) \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to x \sin (x)+\cos (x) (\log (\cos (x))+c_1) \end{align*}

✓ Sympy. Time used: 0.677 (sec). Leaf size: 117

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

\[ y{\left (x \right )} = - C_{1} \tan ^{2}{\left (\frac {x}{2} \right )} + C_{1} + x \tan {\left (\frac {x}{2} \right )} + \frac {\log {\left (\frac {1}{\cos {\left (x \right )} + 1} \right )} \tan ^{2}{\left (\frac {x}{2} \right )}}{2} - \frac {\log {\left (\frac {1}{\cos {\left (x \right )} + 1} \right )}}{2} - \frac {\log {\left (\tan {\left (\frac {x}{2} \right )} - 1 \right )} \tan ^{2}{\left (\frac {x}{2} \right )}}{2} + \frac {\log {\left (\tan {\left (\frac {x}{2} \right )} - 1 \right )}}{2} - \frac {\log {\left (\tan {\left (\frac {x}{2} \right )} + 1 \right )} \tan ^{2}{\left (\frac {x}{2} \right )}}{2} + \frac {\log {\left (\tan {\left (\frac {x}{2} \right )} + 1 \right )}}{2} + \frac {\log {\left (2 \right )} \tan ^{2}{\left (\frac {x}{2} \right )}}{2} - \frac {\log {\left (2 \right )}}{2} \]