28.1.125 problem 148

Internal problem ID [4431]
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 : 148
Date solved : Monday, January 27, 2025 at 09:17:06 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

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

\[ y \left (x \right ) = -\frac {\arcsin \left (x^{2}+c_{1} \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.435 (sec). Leaf size: 19

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

\[ y(x)\to -\frac {\arcsin \left (x^2-c_1\right )}{x} \]