Internal problem ID [3457]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 201.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x y^{\prime }+x \cos \left (\frac {y}{x}\right )^{2}-y=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.492 (sec). Leaf size: 37
DSolve[x y'[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*}