24.1.17 problem 4(b)

Internal problem ID [4206]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 4(b)
Date solved : Monday, January 27, 2025 at 08:42:11 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 34

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

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

✓ Solution by Mathematica

Time used: 0.078 (sec). Leaf size: 42

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

\[ y(x)\to e^{-2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )} \left (-2 \sin (x)-4 \log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )+c_1\right ) \]