Internal problem ID [514]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 37.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2}-3 y^{2}}{2 y x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 45
dsolve(diff(y(x),x) = (x^2-3*y(x)^2)/(2*x*y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {5}\, \sqrt {x \left (x^{5}+5 c_{1}\right )}}{5 x^{2}} \\ y \relax (x ) = \frac {\sqrt {5}\, \sqrt {x \left (x^{5}+5 c_{1}\right )}}{5 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.186 (sec). Leaf size: 50
DSolve[y'[x] == (x^2-3*y[x]^2)/(2*x*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\frac {x^5}{5}+c_1}}{x^{3/2}} \\ y(x)\to \frac {\sqrt {\frac {x^5}{5}+c_1}}{x^{3/2}} \\ \end{align*}