Internal problem ID [15144]
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: 282.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {2 x y \,{\mathrm e}^{x^{2}}+{\mathrm e}^{x^{2}} y^{\prime }=x \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve((2*x*y(x)*exp(x^2)-x*sin(x))+(exp(x^2))*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \left (\sin \left (x \right )-x \cos \left (x \right )+c_{1} \right ) {\mathrm e}^{-x^{2}} \]
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 23
DSolve[(2*x*y[x]*Exp[x^2]-x*Sin[x])+Exp[x^2]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x^2} (\sin (x)-x \cos (x)+c_1) \]