74.6.47 problem 53

Internal problem ID [15999]
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 : 53
Date solved : Monday, March 31, 2025 at 02:24:15 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 59

ode:=5*t*y(t)+4*y(t)^2+1+(t^2+2*t*y(t))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \frac {-t^{3}-\sqrt {t^{6}-t^{4}-4 c_1}}{2 t^{2}} \\ y &= \frac {-t^{3}+\sqrt {t^{6}-t^{4}-4 c_1}}{2 t^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.67 (sec). Leaf size: 84

ode=(5*t*y[t]+4*y[t]^2+1)+(t^2+2*t*y[t])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to -\frac {t^5+\sqrt {t^3} \sqrt {t^7-t^5+4 c_1 t}}{2 t^4} \\ y(t)\to -\frac {t}{2}+\frac {\sqrt {t^3} \sqrt {t^7-t^5+4 c_1 t}}{2 t^4} \\ \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(5*t*y(t) + (t**2 + 2*t*y(t))*Derivative(y(t), t) + 4*y(t)**2 + 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out