29.13.11 problem 365

Internal problem ID [4965]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 365
Date solved : Monday, January 27, 2025 at 09:58:27 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} 2 x^{3} y^{\prime }&=\left (x^{2}-y^{2}\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

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

\begin{align*} y \left (x \right ) &= \frac {x}{\sqrt {c_{1} x -1}} \\ y \left (x \right ) &= -\frac {x}{\sqrt {c_{1} x -1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.275 (sec). Leaf size: 39

DSolve[2 x^3 D[y[x],x]==(x^2-y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x}{\sqrt {-1+c_1 x}} \\ y(x)\to \frac {x}{\sqrt {-1+c_1 x}} \\ y(x)\to 0 \\ \end{align*}