78.1.26 problem 2 (L)

Internal problem ID [18081]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (L)
Date solved : Tuesday, January 28, 2025 at 11:25:44 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)
 

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

✓ Solution by Mathematica

Time used: 0.021 (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*}