Internal problem ID [15138]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 276.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x \sin \left (x \right ) y^{\prime }+\left (\sin \left (x \right )-\cos \left (x \right ) x \right ) y=\sin \left (x \right ) \cos \left (x \right )-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(x*sin(x)*diff(y(x),x)+(sin(x)-x*cos(x))*y(x)=sin(x)*cos(x)-x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sin \left (x \right ) c_{1}}{x}+\cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.127 (sec). Leaf size: 16
DSolve[x*Sin[x]*y'[x]+(Sin[x]-x*Cos[x])*y[x]==Sin[x]*Cos[x]-x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cos (x)+\frac {c_1 \sin (x)}{x} \]