60.1.76 problem 76

Internal problem ID [10090]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 76
Date solved : Monday, January 27, 2025 at 06:26:04 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-a \cos \left (y\right )+b&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 41

dsolve(diff(y(x),x) - a*cos(y(x)) + b=0,y(x), singsol=all)
 

\[ y = 2 \arctan \left (\frac {\tanh \left (\frac {\sqrt {a^{2}-b^{2}}\, \left (x +c_{1} \right )}{2}\right ) \sqrt {a^{2}-b^{2}}}{a +b}\right ) \]

✓ Solution by Mathematica

Time used: 0.265 (sec). Leaf size: 53

DSolve[D[y[x],x] - a*Cos[y[x]] + b==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{b-a \cos (K[1])}dK[1]\&\right ][-x+c_1] \\ y(x)\to -\arccos \left (\frac {b}{a}\right ) \\ y(x)\to \arccos \left (\frac {b}{a}\right ) \\ \end{align*}