Internal problem ID [1918]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x}-\tan \left (\frac {y}{x}\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (6) = \pi ] \end {align*}
✓ Solution by Maple
Time used: 0.464 (sec). Leaf size: 10
dsolve([diff(y(x),x)=y(x)/x+tan(y(x)/x),y(6) = Pi],y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (\frac {x}{12}\right ) x \]
✓ Solution by Mathematica
Time used: 0.954 (sec). Leaf size: 13
DSolve[{y'[x]==y[x]/x+Tan[y[x]/x],y[6]==Pi},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \text {ArcSin}\left (\frac {x}{12}\right ) \\ \end{align*}