Internal problem ID [11404]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {x^{\prime }-\frac {4 t^{2}+3 x^{2}}{2 t x}=0} \]
✓ 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: 0.434 (sec). Leaf size: 34
DSolve[x'[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*}