44.5.12 problem 12

Internal problem ID [7074]
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 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 12
Date solved : Sunday, March 30, 2025 at 11:37:47 AM
CAS classification : [_separable]

\begin{align*} \sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 62

ode:=sin(3*x)+2*y(x)*cos(3*x)^3*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {\sqrt {18 c_1 \cos \left (6 x \right )+18 c_1 -6}\, \sec \left (x \right )}{24 \cos \left (x \right )^{2}-18} \\ y &= \frac {\sqrt {18 c_1 \cos \left (6 x \right )+18 c_1 -6}\, \sec \left (x \right )}{24 \cos \left (x \right )^{2}-18} \\ \end{align*}

✓ Mathematica. Time used: 0.718 (sec). Leaf size: 49

ode=Sin[3*x]+2*y[x]*Cos[3*x]^3*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\sqrt {-\frac {1}{6} \sec ^2(3 x)+2 c_1} \\ y(x)\to \sqrt {-\frac {1}{6} \sec ^2(3 x)+2 c_1} \\ \end{align*}

✓ Sympy. Time used: 0.936 (sec). Leaf size: 46

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x)*cos(3*x)**3*Derivative(y(x), x) + sin(3*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {C_{1} \cos ^{2}{\left (3 x \right )} - 6}}{6 \cos {\left (3 x \right )}}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} \cos ^{2}{\left (3 x \right )} - 6}}{6 \cos {\left (3 x \right )}}\right ] \]