9.1.9 problem 9

Internal problem ID [2849]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 9
Date solved : Tuesday, September 30, 2025 at 05:54:48 AM
CAS classification : [_separable]

\begin{align*} y^{\prime } \tan \left (x \right )-y&=1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

ode:=diff(y(x),x)*tan(x)-y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (x \right ) c_1 -1 \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 17

ode=D[y[x],x]*Tan[x]-y[x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.151 (sec). Leaf size: 8

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

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