Internal problem ID [1681]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 t y y^{\prime }-3 y^{2}+t^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 26
dsolve(2*t*y(t)*diff(y(t),t)=3*y(t)^2-t^2,y(t), singsol=all)
\begin{align*} y \relax (t ) = \sqrt {c_{1} t +1}\, t \\ y \relax (t ) = -\sqrt {c_{1} t +1}\, t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.211 (sec). Leaf size: 34
DSolve[2*t*y[t]*y'[t]==3*y[t]^2-t^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -t \sqrt {1+c_1 t} \\ y(t)\to t \sqrt {1+c_1 t} \\ \end{align*}