24.1.19 problem 4(d)

Internal problem ID [4208]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 4(d)
Date solved : Monday, January 27, 2025 at 08:42:16 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.268 (sec). Leaf size: 38

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

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