Internal problem ID [2622]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, End of chapter, page 61
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {{\mathrm e}^{x} \sin \relax (y)-y \sin \left (y x \right )+\left ({\mathrm e}^{x} \cos \relax (y)-x \sin \left (y x \right )\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ {\mathrm e}^{x} \sin \left (y \relax (x )\right )+\cos \left (x y \relax (x )\right )+c_{1} = 0 \]
✓ 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]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [e^x \sin (y(x))+\cos (x y(x))=c_1,y(x)\right ] \]