Internal problem ID [4765]
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]
\[ \boxed {\cos \left (x \right ) y^{\prime }+y=\cos \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x)*cos(x)+y(x)=cos(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x -\cos \left (x \right )+c_{1} \right ) \left (\cos \left (x \right )-\sin \left (x \right )+1\right )}{\sin \left (x \right )+\cos \left (x \right )+1} \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 25
DSolve[y'[x]*Cos[x]+y[x]==Cos[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )} (x-\cos (x)+c_1) \]