29.37.14 problem 1133

Internal problem ID [5672]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1133
Date solved : Monday, January 27, 2025 at 01:05:48 PM
CAS classification : [_quadrature]

\begin{align*} a \cos \left (y^{\prime }\right )+b y^{\prime }+x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

dsolve(a*cos(diff(y(x),x))+b*diff(y(x),x)+x = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.099 (sec). Leaf size: 42

DSolve[a*Cos[D[y[x],x]] + b*D[y[x],x]+x ==0,y[x],x,IncludeSingularSolutions -> True]
 

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