Internal problem ID [7775]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 196.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } \cos \left (x \right )+y+\left (\sin \left (x \right )+1\right ) \cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(cos(x)*diff(y(x),x) + y(x) + (1 + sin(x))*cos(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-2 \ln \left (\sec \left (x \right )+\tan \left (x \right )\right )+2 \ln \left (\cos \left (x \right )\right )+\sin \left (x \right )+c_{1}}{\sec \left (x \right )+\tan \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.713 (sec). Leaf size: 40
DSolve[Cos[x]*y'[x] + y[x] + (1 + Sin[x])*Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )} \left (\sin (x)+4 \log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )+c_1\right ) \\ \end{align*}