5.12 problem Problem 12

Internal problem ID [2215]

Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.9, Exact Differential Equations. page 91
Problem number: Problem 12.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_exact]

Solve \begin {gather*} \boxed {\sin \relax (y)+\cos \relax (x ) y+\left (x \cos \relax (y)+\sin \relax (x )\right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.031 (sec). Leaf size: 15

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

\[ y \relax (x ) \sin \relax (x )+x \sin \left (y \relax (x )\right )+c_{1} = 0 \]

Solution by Mathematica

Time used: 0.138 (sec). Leaf size: 17

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

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