Internal problem ID [2682]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 47.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {y^{2}+\left (y x +\tan \left (y x \right )\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve((y(x)^2)+(x*y(x)+tan(x*y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\RootOf \left (\textit {\_Z} c_{1} \sin \left (\textit {\_Z} \right )-x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.254 (sec). Leaf size: 14
DSolve[(y[x]^2)+(x*y[x]+Tan[x*y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[y(x) \sin (x y(x))=c_1,y(x)] \]