65.5.4 problem 10.1 (iv)

Internal problem ID [13743]
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 (iv)
Date solved : Tuesday, January 28, 2025 at 06:01:00 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.389 (sec). Leaf size: 22

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

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