Internal problem ID [2877]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 128.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\sqrt {a +b \cos \relax (y)}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 21
dsolve(diff(y(x),x) = sqrt(a+b*cos(y(x))),y(x), singsol=all)
\[ x -\left (\int _{}^{y \relax (x )}\frac {1}{\sqrt {a +b \cos \left (\textit {\_a} \right )}}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.682 (sec). Leaf size: 55
DSolve[y'[x]==Sqrt[a+b Cos[ y[x]]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \text {am}\left (\frac {1}{2} \sqrt {a+b} (x+c_1)|\frac {2 b}{a+b}\right ) \\ y(x)\to -\text {ArcCos}\left (-\frac {a}{b}\right ) \\ y(x)\to \text {ArcCos}\left (-\frac {a}{b}\right ) \\ \end{align*}