78.8.22 problem 22

Internal problem ID [18220]
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. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 11:40:01 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 16

dsolve(exp(x)*sin(y(x))+exp(x)*cos(y(x))*diff(y(x),x)=y(x)*sin(x*y(x))+x*sin(x*y(x))*diff(y(x),x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.528 (sec). Leaf size: 19

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

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