Internal problem ID [5435]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page
20
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {\left (\sin \relax (x ) \sin \relax (y)-x \,{\mathrm e}^{y}\right ) y^{\prime }-{\mathrm e}^{y}-\cos \relax (x ) \cos \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 16
dsolve((sin(x)*sin(y(x))-x*exp(y(x)))*diff(y(x),x)=exp(y(x))+cos(x)*cos(y(x)),y(x), singsol=all)
\[ c_{1}+\sin \relax (x ) \cos \left (y \relax (x )\right )+x \,{\mathrm e}^{y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.965 (sec). Leaf size: 21
DSolve[(Sin[x]*Sin[y[x]]-x*Exp[y[x]])*y'[x]==Exp[y[x]]+Cos[x]*Cos[y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \left (x e^{y(x)}+\sin (x) \cos (y(x))\right )=c_1,y(x)\right ] \]