Internal problem ID [3822]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1135.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime } \sin \left (y^{\prime }\right )+\cos \left (y^{\prime }\right )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.328 (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 \relax (x ) = 1 \\ x -\left (\int _{}^{y \relax (x )}\frac {1}{\RootOf \left (\textit {\_Z} \sin \left (\textit {\_Z} \right )+\cos \left (\textit {\_Z} \right )-\textit {\_a} \right )}d \textit {\_a} \right )-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 28
DSolve[y'[x] Sin[y'[x]]+ Cos[y'[x]]==y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[\{x=\sin (K[1])+c_1,y(x)=K[1] \sin (K[1])+\cos (K[1])\},\{y(x),K[1]\}] \]