62.3.4 problem Ex 4

Internal problem ID [12810]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 10. Homogeneous equations. Page 15
Problem number : Ex 4
Date solved : Tuesday, January 28, 2025 at 04:22:44 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 &= \frac {x^{2}}{\sqrt {-x^{2}+c_{1}}} \\ y &= -\frac {x^{2}}{\sqrt {-x^{2}+c_{1}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.185 (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*}