19.1.1 problem 1

Internal problem ID [3515]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 1
Date solved : Monday, January 27, 2025 at 07:40:10 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 10

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

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

✓ 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*}