13.3.9 problem 9

Internal problem ID [2326]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.4. Page 24
Problem number : 9
Date solved : Monday, January 27, 2025 at 05:45:52 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: 0.041 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.135 (sec). Leaf size: 26

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

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