29.37.17 problem 1137

Internal problem ID [5675]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1137
Date solved : Monday, January 27, 2025 at 01:06:24 PM
CAS classification : [_dAlembert]

\begin{align*} {y^{\prime }}^{2} \left (x +\sin \left (y^{\prime }\right )\right )&=y \end{align*}

✓ Solution by Maple

Time used: 0.926 (sec). Leaf size: 56

dsolve(diff(y(x),x)^2*(x+sin(diff(y(x),x))) = y(x),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= 0 \\ \left [x \left (\textit {\_T} \right ) &= \frac {\left (-\textit {\_T}^{2}+\textit {\_T} \right ) \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 (\left (\textit {\_T} -1\right ) \sin \left (\textit {\_T} \right )+\cos \left (\textit {\_T} \right )-c_{1} \right )}{\left (\textit {\_T} -1\right )^{2}}\right ] \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.144 (sec). Leaf size: 81

DSolve[(D[y[x],x])^2*(x+Sin[D[y[x],x]])==y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\left \{x=\frac {\int \frac {(K[1]-1)^2 \left (2 K[1] \sin (K[1])+K[1]^2 \cos (K[1])\right )}{K[1]-K[1]^2} \, dK[1]}{(K[1]-1)^2}+\frac {c_1}{(K[1]-1)^2},y(x)=x K[1]^2+K[1]^2 \sin (K[1])\right \},\{y(x),K[1]\}\right ] \]