74.6.33 problem 34

Internal problem ID [15977]
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 : Thursday, March 13, 2025 at 07:05:06 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*}

✓ Maple. Time used: 3.029 (sec). Leaf size: 41

ode:=1+5*t-y(t)-(t+2*y(t))*diff(y(t),t) = 0; 
ic:=y(0) = 0; 
dsolve([ode,ic],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*}

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

ode=(1+5*t-y[t])-(t+2*y[t])*D[y[t],t]==0; 
ic={y[0]==0}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 2.459 (sec). Leaf size: 39

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(5*t - (t + 2*y(t))*Derivative(y(t), t) - y(t) + 1,0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = - \frac {t}{2} - \frac {\sqrt {1331 t^{2} + 484 t}}{22}, \ y{\left (t \right )} = - \frac {t}{2} + \frac {\sqrt {1331 t^{2} + 484 t}}{22}\right ] \]