74.6.33 problem 34

Internal problem ID [16056]
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
Date solved : Tuesday, January 28, 2025 at 08:32:01 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 1+5 t -y-\left (t +2 y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 3.029 (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 &= -\frac {t}{2}-\frac {\sqrt {11 t^{2}+4 t}}{2} \\ y &= -\frac {t}{2}+\frac {\sqrt {11 t^{2}+4 t}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.133 (sec). Leaf size: 49

DSolve[{(1+5*t-y[t])-(t+2*y[t])*D[y[t],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*}