29.5.8 problem 123

Internal problem ID [4725]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 123
Date solved : Monday, January 27, 2025 at 09:34:20 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 44

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: 60.123 (sec). Leaf size: 52

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

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