86.3.12 problem 10

Internal problem ID [23103]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 4. Linear equations of the first order. Exercise 4a at page 56
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:21:55 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 11

ode:=diff(y(x),x)+y(x)*tan(x) = sec(x); 
ic:=[y(0) = 5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \left (\tan \left (x \right )+5\right ) \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 12

ode=D[y[x],x]+y[x]*Tan[x]==Sec[x]; 
ic={y[0]==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sin (x)+5 \cos (x) \end{align*}

✓ Sympy. Time used: 0.313 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*tan(x) - sec(x) + Derivative(y(x), x),0) 
ics = {y(0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sin {\left (x \right )} + 5 \cos {\left (x \right )} \]