29.4.22 problem 111

Internal problem ID [4713]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 111
Date solved : Monday, January 27, 2025 at 09:33:40 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 43

dsolve(diff(y(x),x) = a+b*cos(y(x)),y(x), singsol=all)
 

\[ y \left (x \right ) = 2 \arctan \left (\frac {\tan \left (\frac {\sqrt {a^{2}-b^{2}}\, \left (x +c_{1} \right )}{2}\right ) \sqrt {a^{2}-b^{2}}}{a -b}\right ) \]

✓ Solution by Mathematica

Time used: 60.135 (sec). Leaf size: 47

DSolve[D[y[x],x]==a+b Cos[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 \arctan \left (\frac {(a+b) \tanh \left (\frac {1}{2} \sqrt {b^2-a^2} (x+c_1)\right )}{\sqrt {b^2-a^2}}\right ) \]