Internal problem ID [4050]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.37, page 103.
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: 0.004 (sec). Leaf size: 29
dsolve(diff(y(x),x)*cos(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: 0.202 (sec). Leaf size: 40
DSolve[y'[x]*Cos[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*}