Internal problem ID [5466]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page
28
Problem number: 5(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2+3 y^{2} x}{4 x^{2} y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
dsolve(diff(y(x),x)=(2+3*x*y(x)^2)/(4*x^2*y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {5}\, \sqrt {x \left (5 x^{\frac {5}{2}} c_{1}-2\right )}}{5 x} \\ y \relax (x ) = \frac {\sqrt {5}\, \sqrt {x \left (5 x^{\frac {5}{2}} c_{1}-2\right )}}{5 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.057 (sec). Leaf size: 51
DSolve[y'[x]==(2+3*x*y[x]^2)/(4*x^2*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-\frac {2}{5 x}+c_1 x^{3/2}} \\ y(x)\to \sqrt {-\frac {2}{5 x}+c_1 x^{3/2}} \\ \end{align*}