74.2.10 problem 15

Internal problem ID [15851]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 08:09:42 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.215 (sec). Leaf size: 71

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

\[ \text {Solve}\left [\int _1^x(\sin (K[1])+\cos (K[1] y(x)) y(x))dK[1]+\int _1^{y(x)}\left (x \cos (x K[2])-\int _1^x(\cos (K[1] K[2])-K[1] K[2] \sin (K[1] K[2]))dK[1]\right )dK[2]=c_1,y(x)\right ] \]