14.3.12 problem Problem 12

Internal problem ID [3621]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 12
Date solved : Tuesday, September 30, 2025 at 06:48:37 AM
CAS classification : [_linear]

\begin{align*} 1-y \sin \left (x \right )-\cos \left (x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

ode:=1-y(x)*sin(x)-cos(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \cos \left (x \right ) c_1 +\sin \left (x \right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 13

ode=(1-y[x]*Sin[x])-Cos[x]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.435 (sec). Leaf size: 10

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

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