63.4.12 problem 4(d)

Internal problem ID [13055]
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(d)
Date solved : Tuesday, January 28, 2025 at 04:50:23 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.238 (sec). Leaf size: 48

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

\begin{align*} R(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+1}dK[1]\&\right ]\left [\frac {t^2}{2}+t+c_1\right ] \\ R(t)\to -i \\ R(t)\to i \\ \end{align*}