Internal problem ID [6794]
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]]
\[ \boxed {y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.266 (sec). Leaf size: 167
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 {x \left (-i \sqrt {3}-1\right )} \\ y \left (x \right ) &= \sqrt {\left (i \sqrt {3}-1\right ) x} \\ y \left (x \right ) &= -\sqrt {-\left (1+i \sqrt {3}\right ) x} \\ y \left (x \right ) &= -\sqrt {\left (i \sqrt {3}-1\right ) 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 {2^{\frac {2}{3}} \left (-c_{1}^{3}+6 c_{1} x \right )^{\frac {1}{3}}}{2} \\ y \left (x \right ) &= -\frac {2^{\frac {2}{3}} \left (-c_{1}^{3}+6 c_{1} x \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{4} \\ y \left (x \right ) &= \frac {2^{\frac {2}{3}} \left (-c_{1}^{3}+6 c_{1} x \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 70.054 (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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