75.8.19 problem 217

Internal problem ID [16835]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 8. First order not solved for the derivative. Exercises page 67
Problem number : 217
Date solved : Tuesday, January 28, 2025 at 09:34:24 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 16

dsolve(x=diff(y(x),x)+sin(diff(y(x),x)),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: 0.056 (sec). Leaf size: 38

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

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