Internal problem ID [4257]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page
403
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } \cos \relax (x )+y-\left (\cos ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(diff(y(x),x)*cos(x)+y(x)=cos(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {x -\cos \relax (x )+c_{1}}{\sec \relax (x )+\tan \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.128 (sec). Leaf size: 25
DSolve[y'[x]*Cos[x]+y[x]==Cos[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x-\cos (x)+c_1) e^{-2 \tanh ^{-1}\left (\tan \left (\frac {x}{2}\right )\right )} \\ \end{align*}