80.3.2 problem 2

Internal problem ID [18546]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 29. Problems at page 81
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 11:55:39 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} 2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

dsolve(2*x^2*y(x)+y(x)^3-x^3*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {x^{2}}{\sqrt {-x^{2}+c_{1}}} \\ y \left (x \right ) &= -\frac {x^{2}}{\sqrt {-x^{2}+c_{1}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.173 (sec). Leaf size: 47

DSolve[2*x^2*y[x]+y[x]^3-x^3*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x^2}{\sqrt {-x^2+c_1}} \\ y(x)\to \frac {x^2}{\sqrt {-x^2+c_1}} \\ y(x)\to 0 \\ \end{align*}