Internal problem ID [1676]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {3 t^{2}+4 t +2}{-2+2 y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.046 (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)
\[ y \relax (t ) = -\sqrt {\left (2+t \right ) \left (t^{2}+2\right )}+1 \]
✓ Solution by Mathematica
Time used: 0.142 (sec). Leaf size: 22
DSolve[{y'[t] == (3*t^2+4*t+2)/(-2+2*y[t]),y[0]==-1},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 1-\sqrt {(t+2) \left (t^2+2\right )} \\ \end{align*}