19.2.10 problem 10

Internal problem ID [3539]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.6, page 50
Problem number : 10
Date solved : Monday, January 27, 2025 at 07:41:06 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(diff(y(x),x)=sin(x)*(y(x)*sec(x)-2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 20

DSolve[D[y[x],x]==Sin[x]*(y[x]*Sec[x]-2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \sec (x) (\cos (2 x)+2 c_1) \]