Internal problem ID [153]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 33 (a).
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 x^{2}-2 y^{2}}{4 y x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 49
dsolve(diff(y(x),x) = 1/4*(-3*x^2-2*y(x)^2)/(x*y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {2}\, \sqrt {x \left (-x^{3}+2 c_{1}\right )}}{2 x} \\ y \relax (x ) = \frac {\sqrt {2}\, \sqrt {x \left (-x^{3}+2 c_{1}\right )}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.241 (sec). Leaf size: 60
DSolve[y'[x] == 1/4*(-3*x^2-2*y[x]^2)/(x*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x^3+2 c_1}}{\sqrt {2} \sqrt {x}} \\ y(x)\to \frac {\sqrt {-x^3+2 c_1}}{\sqrt {2} \sqrt {x}} \\ \end{align*}