Internal problem ID [11687]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {{\mathrm e}^{x} \sin \left (y\right )+y+\left ({\mathrm e}^{x} \cos \left (y\right )+x +{\mathrm e}^{y}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) x +{\mathrm e}^{x} \sin \left (y \left (x \right )\right )+{\mathrm e}^{y \left (x \right )}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.637 (sec). Leaf size: 22
DSolve[Exp[x]*Sin[y[x]]+y[x]+ (Exp[x]*Cos[y[x]]+x+Exp[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [e^{y(x)}+x y(x)+e^x \sin (y(x))=c_1,y(x)\right ] \]