Internal problem ID [6041]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 97. The p-discriminant equation. EXERCISES
Page 314
Problem number: 16.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{4} \left (y^{\prime }\right )^{3}-6 x y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.334 (sec). Leaf size: 123
dsolve(y(x)^4*diff(y(x),x)^3-6*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {2}\, \sqrt {x} \\ y \relax (x ) = -\sqrt {2}\, \sqrt {x} \\ y \relax (x ) = 0 \\ y \relax (x ) = \frac {\left (-4 c_{1}^{3}+24 c_{1} x \right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = -\frac {\left (-4 c_{1}^{3}+24 c_{1} x \right )^{\frac {1}{3}}}{4}-\frac {i \sqrt {3}\, \left (-4 c_{1}^{3}+24 c_{1} x \right )^{\frac {1}{3}}}{4} \\ y \relax (x ) = -\frac {\left (-4 c_{1}^{3}+24 c_{1} x \right )^{\frac {1}{3}}}{4}+\frac {i \sqrt {3}\, \left (-4 c_{1}^{3}+24 c_{1} x \right )^{\frac {1}{3}}}{4} \\ y \relax (x ) = c_{1} \sqrt {x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 74.251 (sec). Leaf size: 22649
DSolve[y[x]^4*(y'[x])^3-6*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
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