74.8.39 problem 40 (b)

Internal problem ID [16175]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 40 (b)
Date solved : Tuesday, January 28, 2025 at 08:56:15 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {t}{y^{3}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 44

dsolve([diff(y(t),t)=t/y(t)^3,y(0) = 0],y(t), singsol=all)
 

\begin{align*} y &= 2^{{1}/{4}} \sqrt {t} \\ y &= -2^{{1}/{4}} \sqrt {t} \\ y &= -i 2^{{1}/{4}} \sqrt {t} \\ y &= i 2^{{1}/{4}} \sqrt {t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.198 (sec). Leaf size: 76

DSolve[{D[y[t],t]==t/y[t]^3,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -\sqrt [4]{2} \sqrt [4]{t^2} \\ y(t)\to -i \sqrt [4]{2} \sqrt [4]{t^2} \\ y(t)\to i \sqrt [4]{2} \sqrt [4]{t^2} \\ y(t)\to \sqrt [4]{2} \sqrt [4]{t^2} \\ \end{align*}