26.5.18 problem 22

Internal problem ID [4292]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, End of chapter, page 61
Problem number : 22
Date solved : Monday, January 27, 2025 at 08:49:23 AM
CAS classification : [_exact]

\begin{align*} {\mathrm e}^{x} \sin \left (y\right )-y \sin \left (y x \right )+\left ({\mathrm e}^{x} \cos \left (y\right )-x \sin \left (y x \right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 16

dsolve((exp(x)*sin(y(x))-y(x)*sin(x*y(x)))+(exp(x)*cos(y(x))-x*sin(x*y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.558 (sec). Leaf size: 19

DSolve[(Exp[x]*Sin[y[x]]-y[x]*Sin[x*y[x]])+(Exp[x]*Cos[y[x]]-x*Sin[x*y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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