78.6.18 problem 8

Internal problem ID [18186]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 10 (Linear equations). Problems at page 82
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 11:37:30 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

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

\[ y = c_1 \tan \left (x \right )-\sec \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 15

DSolve[D[y[x],x]*Sin[2*x]==2*y[x]+2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sec (x) (-1+c_1 \sin (x)) \]