60.1.564 problem 567

Internal problem ID [10578]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 567
Date solved : Monday, January 27, 2025 at 09:16:28 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 18

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

\[ y = \int \operatorname {RootOf}\left (a \cos \left (\textit {\_Z} \right )+\textit {\_Z} b +x \right )d x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 42

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

\[ \text {Solve}[\{y(x)=\int K[1] (a \sin (K[1])-b) \, dK[1]+c_1,x=-a \cos (K[1])-b K[1]\},\{y(x),K[1]\}] \]