74.7.25 problem 25

Internal problem ID [16031]
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 : 25
Date solved : Monday, March 31, 2025 at 02:31:10 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 2 t^{2}-7 t y+5 y^{2}+t y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.202 (sec). Leaf size: 52

ode:=2*t^2-7*t*y(t)+5*y(t)^2+t*y(t)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {t \left (-2 t^{2} c_1 +\operatorname {RootOf}\left (\textit {\_Z}^{4}-3 t^{2} c_1 +2 \textit {\_Z} \right )\right )}{-3 t^{2} c_1 +2 \operatorname {RootOf}\left (\textit {\_Z}^{4}-3 t^{2} c_1 +2 \textit {\_Z} \right )} \]

✓ Mathematica. Time used: 0.088 (sec). Leaf size: 42

ode=(2*t^2-7*t*y[t]+5*y[t]^2)+(t*y[t])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {K[1]}{(2 K[1]-1) (3 K[1]-2)}dK[1]=-\log (t)+c_1,y(t)\right ] \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t**2 + t*y(t)*Derivative(y(t), t) - 7*t*y(t) + 5*y(t)**2,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out