Internal problem ID [8147]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 567.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {a \cos \left (y^{\prime }\right )+y^{\prime } b +x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(a*cos(diff(y(x),x))+b*diff(y(x),x)+x=0,y(x), singsol=all)
\[ y \relax (x ) = \int \RootOf \left (a \cos \left (\textit {\_Z} \right )+b \textit {\_Z} +x \right )d x +c_{1} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 49
DSolve[x + a*Cos[y'[x]] + b*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{y(x)=a \sin (K[1])-a K[1] \cos (K[1])-\frac {1}{2} b K[1]^2+c_1,x=-a \cos (K[1])-b K[1]\right \},\{y(x),K[1]\}\right ] \]