35.9.4 problem 2, using elementary method

Internal problem ID [6239]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 2, using elementary method
Date solved : Monday, January 27, 2025 at 01:49:48 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=3 x^{2} y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 10

dsolve(diff(y(x),x)=3*x^2*y(x),y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 18

DSolve[D[y[x],x]==3*x^2*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{x^3} \\ y(x)\to 0 \\ \end{align*}