71.3.12 problem 7

Internal problem ID [14362]
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 : 7
Date solved : Tuesday, January 28, 2025 at 06:27:40 AM
CAS classification : [_separable]

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

Solution by Maple

Time used: 0.002 (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: 0.023 (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*}