Internal problem ID [3462]
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]
\[ \boxed {x y^{\prime }-y-x \sec \left (\frac {y}{x}\right )^{2}=0} \]
✓ 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)
\[ \frac {\cos \left (\frac {y \left (x \right )}{x}\right ) \sin \left (\frac {y \left (x \right )}{x}\right ) x +y \left (x \right )}{2 x}-\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.255 (sec). Leaf size: 31
DSolve[x y'[x]==y[x]+x Sec[y[x]/x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)}{2 x}+\frac {1}{4} \sin \left (\frac {2 y(x)}{x}\right )=\log (x)+c_1,y(x)\right ] \]