Internal problem ID [4327]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1132.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_Clairaut]
\[ \boxed {\cos \left (y^{\prime }\right )+x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(cos(diff(y(x),x))+x*diff(y(x),x) = y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \arcsin \left (x \right ) x +\sqrt {-x^{2}+1} y \left (x \right ) = \cos \left (c_{1} \right )+c_{1} x \end{align*}
✓ Solution by Mathematica
Time used: 0.051 (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*}