63.5.23 problem 8

Internal problem ID [13097]
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 : 8
Date solved : Tuesday, January 28, 2025 at 04:52:12 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 16

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

\[ x \left (t \right ) = -t -\tan \left (-t +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.513 (sec). Leaf size: 14

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

\[ x(t)\to -t+\tan (t+c_1) \]