63.4.9 problem 4(a)

Internal problem ID [13052]
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 1.3.1 Separable equations. Exercises page 26
Problem number : 4(a)
Date solved : Tuesday, January 28, 2025 at 04:50:15 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=\frac {2 x}{1+t} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 11

dsolve(diff(x(t),t)=2*x(t)/(t+1),x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 18

DSolve[D[x[t],t]==2*x[t]/(t+1),x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_1 (t+1)^2 \\ x(t)\to 0 \\ \end{align*}