Internal problem ID [14322]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number: 34.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y-\left (t +2 y\right ) y^{\prime }=-5 t -1} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 1.266 (sec). Leaf size: 41
dsolve([(1+5*t-y(t))-(t+2*y(t))*diff(y(t),t)=0,y(0) = 0],y(t), singsol=all)
\begin{align*} y \left (t \right ) &= -\frac {t}{2}-\frac {\sqrt {11 t^{2}+4 t}}{2} \\ y \left (t \right ) &= -\frac {t}{2}+\frac {\sqrt {11 t^{2}+4 t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.135 (sec). Leaf size: 49
DSolve[{(1+5*t-y[t])-(t+2*y[t])*y'[t]==0,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {t}{2}-\frac {1}{2} \sqrt {t (11 t+4)} \\ y(t)\to \frac {1}{2} \left (\sqrt {t (11 t+4)}-t\right ) \\ \end{align*}