Internal problem ID [3476]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 743.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.067 (sec). Leaf size: 24
dsolve(x*(x-y(x)*tan(y(x)/x))*diff(y(x),x)+(x+y(x)*tan(y(x)/x))*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{\cos \left (\RootOf \left (\textit {\_Z} \cos \left (\textit {\_Z} \right ) x^{2}-c_{1}\right )\right ) x} \]
✓ Solution by Mathematica
Time used: 0.327 (sec). Leaf size: 31
DSolve[x(x-y[x] Tan[y[x]/x])y'[x]+(x+y[x] Tan[y[x]/x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\log \left (\frac {y(x)}{x}\right )-\log \left (\cos \left (\frac {y(x)}{x}\right )\right )=2 \log (x)+c_1,y(x)\right ] \]