63.5.20 problem 5

Internal problem ID [13094]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises page 41
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 04:52:06 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

\[ x \left (t \right ) = c_{1} {\mathrm e}^{t^{2}} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 18

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

\begin{align*} x(t)\to c_1 e^{t^2} \\ x(t)\to 0 \\ \end{align*}