14.2.9 problem 9

Internal problem ID [2497]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 9
Date solved : Monday, January 27, 2025 at 05:54:31 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {3 t^{2}+4 t +2}{-2+2 y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 19

dsolve([diff(y(t),t)=(3*t^2+4*t+2)/(2*(y(t)-1)),y(0) = -1],y(t), singsol=all)
 

\[ y = -\sqrt {\left (2+t \right ) \left (t^{2}+2\right )}+1 \]

✓ Solution by Mathematica

Time used: 0.158 (sec). Leaf size: 26

DSolve[{D[y[t],t]==(3*t^2+4*t+2)/(2*(y[t]-1)),{y[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 1-\sqrt {t^3+2 t^2+2 t+4} \]