Internal problem ID [3369]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 111.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-b \cos \left (y\right )=a} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 43
dsolve(diff(y(x),x) = a+b*cos(y(x)),y(x), singsol=all)
\[ y \left (x \right ) = 2 \arctan \left (\frac {\tan \left (\frac {\sqrt {a^{2}-b^{2}}\, \left (c_{1} +x \right )}{2}\right ) \sqrt {a^{2}-b^{2}}}{a -b}\right ) \]
✓ Solution by Mathematica
Time used: 60.13 (sec). Leaf size: 47
DSolve[y'[x]==a+b Cos[y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 \arctan \left (\frac {(a+b) \tanh \left (\frac {1}{2} \sqrt {b^2-a^2} (x+c_1)\right )}{\sqrt {b^2-a^2}}\right ) \]