74.4.46 problem 46

Internal problem ID [15939]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 46
Date solved : Tuesday, January 28, 2025 at 08:23:41 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&=\sqrt {\frac {y}{t}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.633 (sec). Leaf size: 94

dsolve([diff(y(t),t)=sqrt(y(t)/t),y(1) = 2],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.170 (sec). Leaf size: 57

DSolve[{D[y[t],t]==Sqrt[y[t]/t],{y[1]==2}},y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to t-2 \left (1+\sqrt {2}\right ) \sqrt {t}+2 \sqrt {2}+3 \\ y(t)\to t+2 \left (\sqrt {2}-1\right ) \sqrt {t}-2 \sqrt {2}+3 \\ \end{align*}