63.4.27 problem 21

Internal problem ID [13070]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 04:51:15 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{\prime }&=\frac {4 t^{2}+3 x^{2}}{2 x t} \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 26

dsolve(diff(x(t),t)=(4*t^2+3*x(t)^2)/(2*t*x(t)),x(t), singsol=all)
 

\begin{align*} x \left (t \right ) &= \sqrt {c_{1} t -4}\, t \\ x \left (t \right ) &= -\sqrt {c_{1} t -4}\, t \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.318 (sec). Leaf size: 34

DSolve[D[x[t],t]==(4*t^2+3*x[t]^2)/(2*t*x[t]),x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to -t \sqrt {-4+c_1 t} \\ x(t)\to t \sqrt {-4+c_1 t} \\ \end{align*}