74.7.10 problem 10

Internal problem ID [16087]
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 : 10
Date solved : Tuesday, January 28, 2025 at 08:38:43 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime }-\frac {y}{t}&=t^{2} y^{{3}/{2}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(diff(y(t),t)-1/t*y(t)=t^2*y(t)^(3/2),y(t), singsol=all)
 

\[ \frac {1}{\sqrt {y}}+\frac {t^{3}}{7}-\frac {c_{1}}{\sqrt {t}} = 0 \]

✓ Solution by Mathematica

Time used: 0.156 (sec). Leaf size: 25

DSolve[D[y[t],t]-1/t*y[t]==t^2*y[t]^(3/2),y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {49 t}{\left (t^{7/2}-7 c_1\right ){}^2} \\ y(t)\to 0 \\ \end{align*}