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]
Solve \begin {gather*} \boxed {y^{\prime }-a -b \sin \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 56
dsolve(diff(y(x),x) = a+b*sin(y(x)),y(x), singsol=all)
\[ y \relax (x ) = -2 \arctan \left (\frac {-\tan \left (\frac {c_{1} \sqrt {a^{2}-b^{2}}}{2}+\frac {x \sqrt {a^{2}-b^{2}}}{2}\right ) \sqrt {a^{2}-b^{2}}+b}{a}\right ) \]
✓ Solution by Mathematica
Time used: 60.166 (sec). Leaf size: 52
DSolve[y'[x]==a+b Sin[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \text {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*}