36.1.8 problem 8

Internal problem ID [6263]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 8
Date solved : Monday, January 27, 2025 at 01:50:28 PM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

\[ x \left (t \right ) = c_{1} {\mathrm e}^{t^{3}} \]

✓ Solution by Mathematica

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

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

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