8.6.33 problem 33 (a)

Internal problem ID [803]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 33 (a)
Date solved : Wednesday, February 05, 2025 at 04:21:09 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{\prime }&=\frac {-3 x^{2}-2 y^{2}}{4 x y} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 47

dsolve(diff(y(x),x) = 1/4*(-3*x^2-2*y(x)^2)/(x*y(x)),y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {2}\, \sqrt {-x \left (x^{3}-2 c_1 \right )}}{2 x} \\ y &= \frac {\sqrt {2}\, \sqrt {-x \left (x^{3}-2 c_1 \right )}}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.215 (sec). Leaf size: 60

DSolve[D[y[x],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*}