29.37.13 problem 1132

Internal problem ID [5671]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1132
Date solved : Monday, January 27, 2025 at 01:05:46 PM
CAS classification : [_Clairaut]

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

✓ Solution by Maple

Time used: 0.007 (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: 0.033 (sec). Leaf size: 18

DSolve[Cos[D[y[x],x]]+x*D[y[x],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*}