38.2.39 problem 39

Internal problem ID [6468]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 39
Date solved : Monday, January 27, 2025 at 02:06:51 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 45

dsolve(2*x*y(x)*diff(y(x),x)=x^2-y(x)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.210 (sec). Leaf size: 56

DSolve[2*x*y[x]*D[y[x],x]==x^2-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {x^3+3 c_1}}{\sqrt {3} \sqrt {x}} \\ y(x)\to \frac {\sqrt {x^3+3 c_1}}{\sqrt {3} \sqrt {x}} \\ \end{align*}