74.6.1 problem 1

Internal problem ID [16024]
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 : Tuesday, January 28, 2025 at 08:26:50 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 57

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

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

✓ Solution by Mathematica

Time used: 17.378 (sec). Leaf size: 105

DSolve[(y[t]^2-y[t]/(2*Sqrt[t]))+(2*t*y[t]-Sqrt[t]+1)*D[y[t],t]==0,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*}