71.3.8 problem 4 (H)

Internal problem ID [14358]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 4 (H)
Date solved : Tuesday, January 28, 2025 at 06:27:34 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=-y x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

dsolve(diff(y(x),x)=-x*y(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x^{2}}{2}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 22

DSolve[D[y[x],x]==-x*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{-\frac {x^2}{2}} \\ y(x)\to 0 \\ \end{align*}