Internal problem ID [12972]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.6 page 89
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\cos \left (y\right )=1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 10
dsolve(diff(y(t),t)=1+cos(y(t)),y(t), singsol=all)
\[ y \left (t \right ) = 2 \arctan \left (t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.462 (sec). Leaf size: 35
DSolve[y'[t]==1+cos[y[t]],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\cos (K[1])+1}dK[1]\&\right ][t+c_1] \\ y(t)\to \cos ^{(-1)}(-1) \\ \end{align*}