72.5.22 problem 9

Internal problem ID [14708]
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
Date solved : Tuesday, January 28, 2025 at 07:12:14 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=1+\cos \left (y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 10

dsolve(diff(y(t),t)=1+cos(y(t)),y(t), singsol=all)
 

\[ y = 2 \arctan \left (t +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.243 (sec). Leaf size: 35

DSolve[D[y[t],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*}