Internal problem ID [2872]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 123.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-a -b \sin \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 43
dsolve(diff(y(x),x) = a+b*sin(y(x)),y(x), singsol=all)
\[ y \left (x \right ) = -2 \arctan \left (\frac {b -\tan \left (\frac {\sqrt {a^{2}-b^{2}}\, \left (x +c_{1} \right )}{2}\right ) \sqrt {a^{2}-b^{2}}}{a}\right ) \]
✓ Solution by Mathematica
Time used: 60.182 (sec). Leaf size: 52
DSolve[y'[x]==a+b Sin[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \arctan \left (\frac {-b+\sqrt {(a-b) (a+b)} \tan \left (\frac {1}{2} \sqrt {(a-b) (a+b)} (x+c_1)\right )}{a}\right ) \\ \end{align*}