Internal problem ID [3823]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1137.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [_dAlembert]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2} \left (x +\sin \left (y^{\prime }\right )\right )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 1.25 (sec). Leaf size: 68
dsolve(diff(y(x),x)^2*(x+sin(diff(y(x),x))) = y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ \left [x \left (\textit {\_T} \right ) = \frac {-\textit {\_T}^{2} \sin \left (\textit {\_T} \right )+\textit {\_T} \sin \left (\textit {\_T} \right )-\cos \left (\textit {\_T} \right )+c_{1}}{\left (\textit {\_T} -1\right )^{2}}, y \left (\textit {\_T} \right ) = \frac {\textit {\_T}^{2} \left (-\textit {\_T}^{2} \sin \left (\textit {\_T} \right )+\textit {\_T} \sin \left (\textit {\_T} \right )-\cos \left (\textit {\_T} \right )+c_{1}\right )}{\left (\textit {\_T} -1\right )^{2}}+\textit {\_T}^{2} \sin \left (\textit {\_T} \right )\right ] \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.116 (sec). Leaf size: 61
DSolve[(y'[x])^2 (x+Sin[y'[x]])==y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=\frac {-(K[1]-1) K[1] \sin (K[1])-\cos (K[1])}{(K[1]-1)^2}+\frac {c_1}{(K[1]-1)^2},y(x)=x K[1]^2+K[1]^2 \sin (K[1])\right \},\{y(x),K[1]\}\right ] \]