68.6.1 problem 1

Internal problem ID [17311]
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 : 1
Date solved : Thursday, October 02, 2025 at 02:01:26 PM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 57

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

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

✓ Mathematica. Time used: 16.997 (sec). Leaf size: 105

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

\begin{align*} y(t)&\to \frac {t^{3/4}-\sqrt [4]{t}-\sqrt {\sqrt {t} \left (t-2 \sqrt {t}+4 c_1 t+1\right )}}{2 t^{5/4}}\\ y(t)&\to \frac {t^{3/4}-\sqrt [4]{t}+\sqrt {\sqrt {t} \left (t-2 \sqrt {t}+4 c_1 t+1\right )}}{2 t^{5/4}} \end{align*}

✗ Sympy

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

Timed Out