89.5.22 problem 22

Internal problem ID [24372]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 22
Date solved : Thursday, October 02, 2025 at 10:22:29 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=1+3 y \tan \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(y(x),x) = 1+3*tan(x)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\tan \left (x \right )}{3}+c_1 \sec \left (x \right )^{3}+\frac {2 \tan \left (x \right ) \sec \left (x \right )^{2}}{3} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 26

ode=D[y[x],x]== 1+3*y[x]*Tan[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{12} \sec ^3(x) (9 \sin (x)+\sin (3 x)+12 c_1) \end{align*}

✓ Sympy. Time used: 0.984 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x)*tan(x) + Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} - \frac {\sin ^{3}{\left (x \right )}}{3} + \sin {\left (x \right )}}{\cos ^{3}{\left (x \right )}} \]