13.4.9 problem 11

Internal problem ID [2346]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.9. Page 66
Problem number : 11
Date solved : Monday, January 27, 2025 at 05:49:02 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 3 y t +y^{2}+\left (t^{2}+y t \right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.114 (sec). Leaf size: 21

dsolve([3*t*y(t)+y(t)^2+(t^2+t*y(t))*diff(y(t),t) = 0,y(2) = 1],y(t), singsol=all)
 

\[ y = \frac {-t^{2}+\sqrt {t^{4}+20}}{t} \]

✓ Solution by Mathematica

Time used: 0.675 (sec). Leaf size: 22

DSolve[{3*t*y[t]+y[t]^2+(t^2+t*y[t])*D[y[t],t] == 0,y[2]==1},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\sqrt {t^4+20}}{t}-t \]