62.3.5 problem Ex 5

Internal problem ID [12811]
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 5
Date solved : Tuesday, January 28, 2025 at 04:24:13 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.446 (sec). Leaf size: 45

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

\begin{align*} y(x)\to -\frac {x}{\sqrt {-1-2 c_1 x^2}} \\ y(x)\to \frac {x}{\sqrt {-1-2 c_1 x^2}} \\ y(x)\to 0 \\ \end{align*}