29.37.16 problem 1135

Internal problem ID [5674]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1135
Date solved : Monday, January 27, 2025 at 01:05:49 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.476 (sec). Leaf size: 32

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

\begin{align*} y \left (x \right ) &= 1 \\ x -\int _{}^{y \left (x \right )}\frac {1}{\operatorname {RootOf}\left (\sin \left (\textit {\_Z} \right ) \textit {\_Z} +\cos \left (\textit {\_Z} \right )-\textit {\_a} \right )}d \textit {\_a} -c_{1} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 31

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

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