Internal problem ID [2724]
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]
\[ \boxed {\sin \left (y\right )+y \cos \left (x \right )+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime }=0} \]
✓ 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)
\[ y \left (x \right ) \sin \left (x \right )+x \sin \left (y \left (x \right )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.146 (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]
\[ \text {Solve}[x \sin (y(x))+y(x) \sin (x)=c_1,y(x)] \]