20.3.9 problem Problem 9

Internal problem ID [3618]
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 9
Date solved : Tuesday, March 04, 2025 at 04:54:59 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-y \tan \left (x \right )&=8 \sin \left (x \right )^{3} \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 24

ode:=diff(y(x),x)-y(x)*tan(x) = 8*sin(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = 2 \cos \left (x \right )^{3}-4 \cos \left (x \right )+\frac {\sec \left (x \right ) \left (4 c_{1} +5\right )}{4} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 19

ode=D[y[x],x]-y[x]*Tan[x]==8*Sin[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 2 \sin ^3(x) \tan (x)+c_1 \sec (x) \]

✓ Sympy. Time used: 2.493 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)*tan(x) - 8*sin(x)**3 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + 2 \sin ^{4}{\left (x \right )}}{\cos {\left (x \right )}} \]