63.4.11 problem 4(c)

Internal problem ID [13054]
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(c)
Date solved : Tuesday, January 28, 2025 at 04:50:20 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 45

dsolve((2*u(t)+1)*diff(u(t),t)-(1+t)=0,u(t), singsol=all)
 

\begin{align*} u &= -\frac {1}{2}-\frac {\sqrt {2 t^{2}+4 c_{1} +4 t +1}}{2} \\ u &= -\frac {1}{2}+\frac {\sqrt {2 t^{2}+4 c_{1} +4 t +1}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 59

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

\begin{align*} u(t)\to \frac {1}{2} \left (-1-\sqrt {2 t^2+4 t+1+4 c_1}\right ) \\ u(t)\to \frac {1}{2} \left (-1+\sqrt {2 t^2+4 t+1+4 c_1}\right ) \\ \end{align*}