77.5.3 problem 3

Internal problem ID [20383]
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 (D) at page 16
Problem number : 3
Date solved : Thursday, October 02, 2025 at 05:49:38 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

\[ y = \frac {\left (\tan \left (x \right )+c_1 \right ) \cos \left (x \right )}{x} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 51.367 (sec). Leaf size: 36

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

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