74.7.29 problem 29

Internal problem ID [16106]
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 : 29
Date solved : Tuesday, January 28, 2025 at 08:41:31 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 37

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

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

✓ Solution by Mathematica

Time used: 0.093 (sec). Leaf size: 46

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

\begin{align*} y(t)\to -t \\ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {K[1]-1}{(K[1]-2) K[1]}dK[1]&=-\log (t)+c_1,y(t)\right ] \\ \end{align*}