75.12.8 problem 282

Internal problem ID [16874]
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
Date solved : Tuesday, January 28, 2025 at 09:38:41 AM
CAS classification : [_linear]

\begin{align*} 2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (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)
 

\[ y = \left (\sin \left (x \right )-\cos \left (x \right ) x +c_{1} \right ) {\mathrm e}^{-x^{2}} \]

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 29

DSolve[(2*x*y[x]*Exp[x^2]-x*Sin[x])+Exp[x^2]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x^2} \left (\int _1^xK[1] \sin (K[1])dK[1]+c_1\right ) \]