29.7.26 problem 201

Internal problem ID [4801]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 201
Date solved : Monday, January 27, 2025 at 09:39:54 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }&=y-x \cos \left (\frac {y}{x}\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 12

dsolve(x*diff(y(x),x) = y(x)-x*cos(y(x)/x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = -\arctan \left (\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.438 (sec). Leaf size: 37

DSolve[x D[y[x],x]==y[x]-x Cos[y[x]/x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x \arctan (-\log (x)+2 c_1) \\ y(x)\to -\frac {\pi x}{2} \\ y(x)\to \frac {\pi x}{2} \\ \end{align*}