Internal problem ID [15072]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 7, Total differential equations. The integrating factor. Exercises page
61
Problem number: 184.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {\sin \left (y\right )+\sin \left (x \right ) y+\left (\cos \left (y\right ) x -\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime }=-\frac {1}{x}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve(( sin(y(x))+y(x)*sin(x)+1/x )+( x*cos(y(x))-cos(x)+1/y(x) )*diff(y(x),x)=0,y(x), singsol=all)
\[ -y \left (x \right ) \cos \left (x \right )+\sin \left (y \left (x \right )\right ) x +\ln \left (x \right )+\ln \left (y \left (x \right )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.332 (sec). Leaf size: 23
DSolve[( Sin[y[x]]+y[x]*Sin[x]+1/x )+( x*Cos[y[x]]-Cos[x]+1/y[x] )*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[\log (y(x))+x \sin (y(x))-y(x) \cos (x)+\log (x)=c_1,y(x)] \]