10.2.36 problem 37

Internal problem ID [1164]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 37
Date solved : Monday, January 27, 2025 at 04:37:40 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.005 (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 &= -\frac {\sqrt {5}\, \sqrt {x \left (x^{5}+5 c_1 \right )}}{5 x^{2}} \\ y &= \frac {\sqrt {5}\, \sqrt {x \left (x^{5}+5 c_1 \right )}}{5 x^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 50

DSolve[D[y[x],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*}