78.4.6 problem 7

Internal problem ID [18129]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 8 (Exact Equations). Problems at page 72
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 11:30:11 AM
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: 0.022 (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)
 

\[ c_1 +\cos \left (y\right ) \sin \left (x \right )+x \,{\mathrm e}^{y} = 0 \]

✓ Solution by Mathematica

Time used: 0.624 (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]
 

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