74.6.46 problem 52

Internal problem ID [16069]
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 : 52
Date solved : Tuesday, January 28, 2025 at 08:35:14 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 51

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

\begin{align*} y &= \frac {1+\sqrt {-2 c_{1} t^{2}-4 t^{3}+1}}{t} \\ y &= \frac {1-\sqrt {-2 c_{1} t^{2}-4 t^{3}+1}}{t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.505 (sec). Leaf size: 68

DSolve[(y[t]+2*t^2)+(t^2*y[t]-t)*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {1}{t}-\sqrt {\frac {1}{t^2}} \sqrt {-4 t^3+c_1 t^2+1} \\ y(t)\to \frac {1}{t}+\sqrt {\frac {1}{t^2}} \sqrt {-4 t^3+c_1 t^2+1} \\ \end{align*}