40.6.9 problem 18

Internal problem ID [6689]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 10. Singular solutions, Extraneous loci. Supplemetary problems. Page 74
Problem number : 18
Date solved : Monday, January 27, 2025 at 02:22:39 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.118 (sec). Leaf size: 40

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

\begin{align*} y &= -\frac {2 \sqrt {3}\, x^{3}}{9} \\ y &= \frac {2 \sqrt {3}\, x^{3}}{9} \\ y &= \frac {x^{2}}{2 c_1}-\frac {1}{8 c_1^{3}} \\ \end{align*}

✗ Solution by Mathematica

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

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

Timed out