50.17.2 problem 1(a) solving directly

Internal problem ID [8073]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of First-Order Differential Equations Page 162
Problem number : 1(a) solving directly
Date solved : Monday, January 27, 2025 at 03:43:10 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 y x \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 10

dsolve(diff(y(x),x)=2*x*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 18

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

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