Internal problem ID [7776]
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]
Solve \begin {gather*} \boxed {y^{\prime } \cos \relax (x )+y+\left (1+\sin \relax (x )\right ) \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 29
dsolve(cos(x)*diff(y(x),x) + y(x) + (1 + sin(x))*cos(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\sin \relax (x )+2 \ln \left (\cos \relax (x )\right )-2 \ln \left (\sec \relax (x )+\tan \relax (x )\right )+c_{1}}{\sec \relax (x )+\tan \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.209 (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 \tanh ^{-1}\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*}