Internal problem ID [6040]
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]]
\[ \boxed {y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y=0} \]
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 183
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 \left (x \right ) = \sqrt {-i x \sqrt {3}-x} \\ y \left (x \right ) = \sqrt {i x \sqrt {3}-x} \\ y \left (x \right ) = -\sqrt {-i x \sqrt {3}-x} \\ y \left (x \right ) = -\sqrt {i x \sqrt {3}-x} \\ y \left (x \right ) = \sqrt {x}\, \sqrt {2} \\ y \left (x \right ) = -\sqrt {x}\, \sqrt {2} \\ y \left (x \right ) = 0 \\ y \left (x \right ) = \frac {\left (-4 c_{1}^{3}+24 c_{1} x \right )^{\frac {1}{3}}}{2} \\ y \left (x \right ) = -\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 \left (x \right ) = -\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} \\ \end{align*}
✓ Solution by Mathematica
Time used: 69.212 (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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