Internal problem ID [2954]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 206.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y-x \left (\sec ^{2}\left (\frac {y}{x}\right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 35
dsolve(x*diff(y(x),x) = y(x)+x*sec(y(x)/x)^2,y(x), singsol=all)
\[ \frac {\cos \left (\frac {y \relax (x )}{x}\right ) \sin \left (\frac {y \relax (x )}{x}\right ) x +y \relax (x )}{2 x}-\ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.256 (sec). Leaf size: 31
DSolve[x y'[x]==y[x]+x Sec[y[x]/x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)}{2 x}+\frac {1}{4} \sin \left (\frac {2 y(x)}{x}\right )=\log (x)+c_1,y(x)\right ] \]