Internal problem ID [3972]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number: Recognizable Exact Differential equations. Integrating factors. Exercise 10.5,
page 90.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {{\mathrm e}^{x} \sin \relax (y)+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \relax (y)\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve((exp(x)*sin(y(x))+exp(-y(x)))-(x*exp(-y(x))-exp(x)*cos(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ {\mathrm e}^{x} \sin \left (y \relax (x )\right )+x \,{\mathrm e}^{-y \relax (x )}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.393 (sec). Leaf size: 24
DSolve[(Exp[x]*Sin[y[x]]+Exp[-y[x]])-(x*Exp[-y[x]]-Exp[x]*Cos[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x \left (-e^{-y(x)}\right )-e^x \sin (y(x))=c_1,y(x)\right ] \]