50.4.7 problem 7

Internal problem ID [7856]
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
Date solved : Monday, January 27, 2025 at 03:26:39 PM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.032 (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)
 

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

✓ Solution by Mathematica

Time used: 0.634 (sec). Leaf size: 21

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

\[ \text {Solve}\left [2 \left (x e^{y(x)}+\sin (x) \cos (y(x))\right )=c_1,y(x)\right ] \]