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 : Monday, January 27, 2025 at 07:47:40 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 19

DSolve[D[y[x],x]-y[x]*Tan[x]==8*Sin[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

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