Internal problem ID [509]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 32.
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 x y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(x),x) = (x^2+3*y(x)^2)/(2*x*y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {x c_{1}-1}\, x \\ y \relax (x ) = -\sqrt {x c_{1}-1}\, x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.27 (sec). Leaf size: 34
DSolve[y'[x] == (x^2+3*y[x]^2)/(2*x*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {-1+c_1 x} \\ y(x)\to x \sqrt {-1+c_1 x} \\ \end{align*}