75.6.4 problem 128

Internal problem ID [16760]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 128
Date solved : Tuesday, January 28, 2025 at 09:21:29 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(diff(y(x),x)+2*x*y(x)=exp(-x^2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 17

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

\[ y(x)\to e^{-x^2} (x+c_1) \]