65.5.3 problem 10.1 (iii)

Internal problem ID [13742]
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)
Date solved : Tuesday, January 28, 2025 at 06:00:31 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.055 (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)
 

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

✓ Solution by Mathematica

Time used: 0.173 (sec). Leaf size: 59

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

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