68.7.17 problem 17

Internal problem ID [17381]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 17
Date solved : Thursday, October 02, 2025 at 02:15:14 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} 2 t +\left (y-3 t \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.068 (sec). Leaf size: 47

ode:=2*t+(y(t)-3*t)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \frac {2 t c_1 -\sqrt {-4 t c_1 +1}+1}{2 c_1} \\ y &= \frac {2 t c_1 +1+\sqrt {-4 t c_1 +1}}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.588 (sec). Leaf size: 76

ode=( 2*t  )+( y[t]-3*t )*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{2} \left (2 t-e^{\frac {c_1}{2}} \sqrt {-4 t+e^{c_1}}+e^{c_1}\right )\\ y(t)&\to \frac {1}{2} \left (2 t+e^{\frac {c_1}{2}} \sqrt {-4 t+e^{c_1}}+e^{c_1}\right ) \end{align*}

✓ Sympy. Time used: 1.190 (sec). Leaf size: 37

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t + (-3*t + y(t))*Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = \frac {C_{1}}{2} + t - \frac {\sqrt {C_{1} \left (C_{1} - 4 t\right )}}{2}, \ y{\left (t \right )} = \frac {C_{1}}{2} + t + \frac {\sqrt {C_{1} \left (C_{1} - 4 t\right )}}{2}\right ] \]