15.7.5 problem 5

Internal problem ID [2986]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 5
Date solved : Monday, January 27, 2025 at 07:05:43 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 39

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

\begin{align*} y &= -\frac {\sqrt {2 x^{4}+4 c_{1}}}{2 x} \\ y &= \frac {\sqrt {2 x^{4}+4 c_{1}}}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.234 (sec). Leaf size: 46

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

\begin{align*} y(x)\to -\frac {\sqrt {\frac {x^4}{2}+c_1}}{x} \\ y(x)\to \frac {\sqrt {\frac {x^4}{2}+c_1}}{x} \\ \end{align*}