62.15.4 problem Ex 4

Internal problem ID [12891]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 26. Equations solvable for \(x\). Page 55
Problem number : Ex 4
Date solved : Tuesday, January 28, 2025 at 04:32:04 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.106 (sec). Leaf size: 29

dsolve(diff(y(x),x)^3-4*x*y(x)*diff(y(x),x)+8*y(x)^2=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {4 x^{3}}{27} \\ y &= 0 \\ y &= \frac {\left (4 c_{1} x -1\right )^{2}}{64 c_{1}^{3}} \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(D[y[x],x])^3-4*x*y[x]*D[y[x],x]+8*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out