8.4.19 problem 19

Internal problem ID [722]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 19
Date solved : Tuesday, March 04, 2025 at 11:34:10 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

\[ y = -\frac {\csc \left (x \right ) \left (2 \cos \left (x \right )^{2}-4 c_1 -1\right )}{4} \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 19

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

\[ y(x)\to -\frac {1}{2} \cos (x) \cot (x)+c_1 \csc (x) \]

✓ Sympy. Time used: 1.150 (sec). Leaf size: 14

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

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