Internal problem ID [515]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {3 y^{2}-x^{2}}{2 y x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 26
dsolve(diff(y(x),x) = (3*y(x)^2-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: 0.208 (sec). Leaf size: 34
DSolve[y'[x] == (3*y[x]^2-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*}