60.1.563 problem 566

Internal problem ID [10577]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 566
Date solved : Monday, January 27, 2025 at 09:16:27 PM
CAS classification : [_quadrature]

\begin{align*} \sin \left (y^{\prime }\right )+y^{\prime }-x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 16

dsolve(sin(diff(y(x),x))+diff(y(x),x)-x=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 38

DSolve[-x + Sin[D[y[x],x]] + D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\left \{x=K[1]+\sin (K[1]),y(x)=\int _1^{K[1]}(\cos (K[1]) K[1]+K[1])dK[1]+c_1\right \},\{y(x),K[1]\}\right ] \]