68.6.46 problem 52

Internal problem ID [17356]
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 : 52
Date solved : Thursday, October 02, 2025 at 02:10:19 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 51

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

\begin{align*} y &= \frac {1+\sqrt {-2 c_1 \,t^{2}-4 t^{3}+1}}{t} \\ y &= \frac {1-\sqrt {-2 c_1 \,t^{2}-4 t^{3}+1}}{t} \\ \end{align*}

✓ Mathematica. Time used: 0.351 (sec). Leaf size: 68

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

\begin{align*} y(t)&\to \frac {1}{t}-\sqrt {\frac {1}{t^2}} \sqrt {-4 t^3+c_1 t^2+1}\\ y(t)&\to \frac {1}{t}+\sqrt {\frac {1}{t^2}} \sqrt {-4 t^3+c_1 t^2+1} \end{align*}

✓ Sympy. Time used: 2.142 (sec). Leaf size: 41

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

\[ \left [ y{\left (t \right )} = \frac {1 - \sqrt {C_{1} t^{2} - 4 t^{3} + 1}}{t}, \ y{\left (t \right )} = \frac {\sqrt {C_{1} t^{2} - 4 t^{3} + 1} + 1}{t}\right ] \]