1.19 problem 4(d)

Internal problem ID [2538]

Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 4(d).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime } \sin \relax (x )+y-\sin \left (2 x \right )=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 29

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

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

Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 29

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

\begin{align*} y(x)\to \cot \left (\frac {x}{2}\right ) \left (-2 \cos (x)+4 \log \left (\cos \left (\frac {x}{2}\right )\right )-2+c_1\right ) \\ \end{align*}