Internal problem ID [1696]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.9. Page 66
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {3 y t +y^{2}+\left (t^{2}+y t \right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.14 (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)
\[ y \relax (t ) = \frac {-t^{2}+\sqrt {t^{4}+20}}{t} \]
✓ Solution by Mathematica
Time used: 0.77 (sec). Leaf size: 22
DSolve[{3*t*y[t]+y[t]^2+(t^2+t*y[t])*y'[t] == 0,y[2]==1},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {\sqrt {t^4+20}}{t}-t \\ \end{align*}