Internal problem ID [5346]
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.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 y x^{3}=0} \]
✓ Solution by Maple
Time used: 0.11 (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 \left (x \right ) &= -\frac {2 \sqrt {3}\, x^{3}}{9} \\ y \left (x \right ) &= \frac {2 \sqrt {3}\, x^{3}}{9} \\ y \left (x \right ) &= \frac {x^{2}}{2 c_{1}}-\frac {1}{8 c_{1}^{3}} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]^3-4*x^4*y'[x]+8*x^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out