Internal problem ID [15110]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8.3. The Lagrange and Clairaut equations. Exercises page 72
Problem number: 222.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_dAlembert]
\[ \boxed {y-2 y^{\prime } x -\sin \left (y^{\prime }\right )=0} \]
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 44
dsolve(y(x)=2*x*diff(y(x),x)+sin(diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ \left [x \left (\textit {\_T} \right ) &= \frac {-\textit {\_T} \sin \left (\textit {\_T} \right )-\cos \left (\textit {\_T} \right )+c_{1}}{\textit {\_T}^{2}}, y \left (\textit {\_T} \right ) &= \frac {-\textit {\_T} \sin \left (\textit {\_T} \right )-2 \cos \left (\textit {\_T} \right )+2 c_{1}}{\textit {\_T}}\right ] \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 47
DSolve[y[x]==2*x*y'[x]+Sin[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=\frac {-K[1] \sin (K[1])-\cos (K[1])}{K[1]^2}+\frac {c_1}{K[1]^2},y(x)=2 x K[1]+\sin (K[1])\right \},\{y(x),K[1]\}\right ] \]