28.1.46 problem 47

Internal problem ID [4352]
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
Date solved : Monday, January 27, 2025 at 09:07:50 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} y^{2}+\left (y x +\tan \left (y x \right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.055 (sec). Leaf size: 18

dsolve((y(x)^2)+(x*y(x)+tan(x*y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (\textit {\_Z} c_{1} \sin \left (\textit {\_Z} \right )-x \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.263 (sec). Leaf size: 14

DSolve[(y[x]^2)+(x*y[x]+Tan[x*y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}[y(x) \sin (x y(x))=c_1,y(x)] \]