13.3.14 problem 16

Internal problem ID [2331]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.4. Page 24
Problem number : 16
Date solved : Monday, January 27, 2025 at 05:46:08 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} 2 t y y^{\prime }&=3 y^{2}-t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (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 &= \sqrt {c_1 t +1}\, t \\ y &= -\sqrt {c_1 t +1}\, t \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.253 (sec). Leaf size: 34

DSolve[2*t*y[t]*D[y[t],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*}