74.6.47 problem 53

Internal problem ID [16070]
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 : 53
Date solved : Tuesday, January 28, 2025 at 08:35:15 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 59

dsolve((5*t*y(t)+4*y(t)^2+1)+(t^2+2*t*y(t))*diff(y(t),t)=0,y(t), singsol=all)
 

\begin{align*} y &= \frac {-t^{3}-\sqrt {t^{6}-t^{4}-4 c_{1}}}{2 t^{2}} \\ y &= \frac {-t^{3}+\sqrt {t^{6}-t^{4}-4 c_{1}}}{2 t^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.670 (sec). Leaf size: 84

DSolve[(5*t*y[t]+4*y[t]^2+1)+(t^2+2*t*y[t])*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -\frac {t^5+\sqrt {t^3} \sqrt {t^7-t^5+4 c_1 t}}{2 t^4} \\ y(t)\to -\frac {t}{2}+\frac {\sqrt {t^3} \sqrt {t^7-t^5+4 c_1 t}}{2 t^4} \\ \end{align*}