Internal problem ID [11686]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number: 10.1 (iii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {\left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }+\sin \left (y\right )-\sin \left (x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve((x*cos(y(x))+cos(x))*diff(y(x),x)+sin(y(x))-y(x)*sin(x)=0,y(x), singsol=all)
\[ \cos \left (x \right ) y \left (x \right )+x \sin \left (y \left (x \right )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.254 (sec). Leaf size: 17
DSolve[(x*Cos[y[x]]+Cos[x])*y'[x]+Sin[y[x]]-y[x]*Sin[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[x \sin (y(x))+y(x) \cos (x)=c_1,y(x)] \]