37.13 problem 1132

Internal problem ID [3819]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 37
Problem number: 1132.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Clairaut]

Solve \begin {gather*} \boxed {\cos \left (y^{\prime }\right )+x y^{\prime }-y=0} \end {gather*}

Solution by Maple

Time used: 0.008 (sec). Leaf size: 27

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

\begin{align*} y \relax (x ) = \arcsin \relax (x ) x +\sqrt {-x^{2}+1} \\ y \relax (x ) = \cos \left (c_{1}\right )+c_{1} x \\ \end{align*}

Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 18

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

\begin{align*} y(x)\to c_1 x+\cos (c_1) \\ y(x)\to 1 \\ \end{align*}