72.8.14 problem 27

Internal problem ID [14778]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page 136
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 07:15:05 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3+y^{2} \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(t),t)= 3+y(t)^2,y(t), singsol=all)
 

\[ y = \sqrt {3}\, \tan \left (\left (t +c_{1} \right ) \sqrt {3}\right ) \]

✓ Solution by Mathematica

Time used: 0.193 (sec). Leaf size: 53

DSolve[D[y[t],t]==3+y[t]^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+3}dK[1]\&\right ][t+c_1] \\ y(t)\to -i \sqrt {3} \\ y(t)\to i \sqrt {3} \\ \end{align*}