Internal problem ID [3095]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 8, page 41
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime }-{\mathrm e}^{y}-\cos \left (x \right ) \cos \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.047 (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)
\[ c_{1} +\sin \left (x \right ) \cos \left (y \left (x \right )\right )+{\mathrm e}^{y \left (x \right )} x = 0 \]
✓ Solution by Mathematica
Time used: 0.626 (sec). Leaf size: 21
DSolve[(Sin[x]*Sin[y[x]]-x*Exp[y[x]])*y'[x]==Exp[y[x]]+Cos[x]*Cos[y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \left (x e^{y(x)}+\sin (x) \cos (y(x))\right )=c_1,y(x)\right ] \]