83.8.19 problem 20

Internal problem ID [19145]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 01:05:29 PM
CAS classification : [_exact]

\begin{align*} y \left (1+\frac {1}{x}\right )+\cos \left (y\right )+\left (x +\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 17

dsolve(y(x)*(1+1/x)+cos(y(x))+(x+ln(x)-x*sin(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.256 (sec). Leaf size: 22

DSolve[y[x]*(1+1/x)+Cos[y[x]]+(x+Log[x]-x*Sin[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}[y(x) (-\log (x))-x (y(x)+\cos (y(x)))=c_1,y(x)] \]