Internal problem ID [549]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {{\mathrm e}^{x} \sin \relax (y)-2 \sin \relax (x ) y+\left (2 \cos \relax (x )+{\mathrm e}^{x} \cos \relax (y)\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(exp(x)*sin(y(x))-2*sin(x)*y(x)+(2*cos(x)+exp(x)*cos(y(x)))*diff(y(x),x) = 0,y(x), singsol=all)
\[ {\mathrm e}^{x} \sin \left (y \relax (x )\right )+2 \cos \relax (x ) y \relax (x )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.273 (sec). Leaf size: 20
DSolve[Exp[x]*Sin[y[x]]-2*Sin[x]*y[x]+(2*Cos[x]+Exp[x]*Cos[y[x]])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [e^x \sin (y(x))+2 y(x) \cos (x)=c_1,y(x)\right ] \]