14.2.15 problem 16

Internal problem ID [2503]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 16
Date solved : Monday, January 27, 2025 at 05:54:50 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: 0.201 (sec). Leaf size: 127

DSolve[2*t*D[y[t],t]==3*y[t]^2-t^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {i t \left (c_1 \operatorname {BesselJ}\left (1,\frac {1}{2} i \sqrt {3} t\right )-\operatorname {BesselY}\left (1,-\frac {1}{2} i \sqrt {3} t\right )\right )}{\sqrt {3} \left (\operatorname {BesselY}\left (0,-\frac {1}{2} i \sqrt {3} t\right )+c_1 \operatorname {BesselJ}\left (0,\frac {1}{2} i \sqrt {3} t\right )\right )} \\ y(t)\to \frac {i t \operatorname {BesselJ}\left (1,\frac {1}{2} i \sqrt {3} t\right )}{\sqrt {3} \operatorname {BesselJ}\left (0,\frac {1}{2} i \sqrt {3} t\right )} \\ \end{align*}