29.2.2 problem 27

Internal problem ID [4635]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 27
Date solved : Sunday, March 30, 2025 at 03:31:45 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

\[ y = \frac {\left (2 c_1 +x \right ) \sec \left (x \right )}{2}+\frac {\sin \left (x \right )}{2} \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{2} (\sin (x)+(x+2 c_1) \sec (x)) \]

✓ Sympy. Time used: 0.856 (sec). Leaf size: 17

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)
 

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x}{2} + \frac {\sin {\left (2 x \right )}}{4}}{\cos {\left (x \right )}} \]