15.1.5 problem 5

Internal problem ID [2845]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 5
Date solved : Monday, January 27, 2025 at 06:19:42 AM
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*}