29.37.15 problem 1134

Internal problem ID [5673]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1134
Date solved : Monday, January 27, 2025 at 01:05:48 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 16

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

\[ y \left (x \right ) = \int \operatorname {RootOf}\left (\sin \left (\textit {\_Z} \right )+\textit {\_Z} -x \right )d x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 38

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

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