12.4.6 problem 6

Internal problem ID [1613]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear Equations. Section 2.3 Page 60
Problem number : 6
Date solved : Monday, January 27, 2025 at 05:13:58 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (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: 0.022 (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*}