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 : Monday, January 27, 2025 at 02:47:00 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 62

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

\begin{align*} y &= -\frac {\sec \left (x \right ) \sqrt {18 c_{1} \cos \left (6 x \right )+18 c_{1} -6}}{24 \cos \left (x \right )^{2}-18} \\ y &= \frac {\sec \left (x \right ) \sqrt {18 c_{1} \cos \left (6 x \right )+18 c_{1} -6}}{24 \cos \left (x \right )^{2}-18} \\ \end{align*}

✓ Solution by Mathematica

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

DSolve[Sin[3*x]+2*y[x]*Cos[3*x]^3*D[y[x],x]==0,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*}