29.7.30 problem 205

Internal problem ID [4805]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 205
Date solved : Monday, January 27, 2025 at 09:40:11 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }-y+x \sec \left (\frac {y}{x}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 12

dsolve(x*diff(y(x),x)-y(x)+x*sec(y(x)/x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.457 (sec). Leaf size: 15

DSolve[x D[y[x],x]-y[x]+x Sec[y[x]/x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \arcsin (-\log (x)+c_1) \]