Internal problem ID [2349]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 38, page 173
Problem number: 12.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {{y^{\prime }}^{3}+y^{\prime } x y-2 y^{2}=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 28
dsolve(diff(y(x),x)^3+diff(y(x),x)*x*y(x)=2*y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {x^{3}}{27} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (c_{1} x +1\right )^{2}}{4 c_{1}^{3}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 141.328 (sec). Leaf size: 10666
DSolve[y'[x]^3+y'[x]*x*y[x]==2*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
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