38.6.36 problem 36

Internal problem ID [8466]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 36
Date solved : Tuesday, September 30, 2025 at 05:37:36 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\tan \left (x \right ) y&=\cos \left (x \right )^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 11

ode:=diff(y(x),x)+tan(x)*y(x) = cos(x)^2; 
ic:=[y(0) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 20

ode=D[y[x],x]+Tan[x]*y[x]==Cos[x]^2; 
ic={y[0]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \cos (x) \left (\int _0^x\cos (K[1])dK[1]-1\right ) \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) - cos(x)**2 + Derivative(y(x), x),0) 
ics = {y(0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

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