63.4.14 problem 4(f)

Internal problem ID [13057]
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(f)
Date solved : Tuesday, January 28, 2025 at 04:50:39 AM
CAS classification : [_separable]

\begin{align*} \left (1+t \right ) x^{\prime }+x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

dsolve((1+t)*diff(x(t),t)+x(t)^2=0,x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {1}{\ln \left (t +1\right )+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.164 (sec). Leaf size: 21

DSolve[(1+t)*D[x[t],t]+x[t]^2==0,x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{\log (t+1)-c_1} \\ x(t)\to 0 \\ \end{align*}