Internal problem ID [6120]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number: 10.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 y^{2} \left (y^{\prime }\right )^{3}-2 x y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.317 (sec). Leaf size: 95
dsolve(4*y(x)^2*diff(y(x),x)^3-2*x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {2^{\frac {3}{4}} 3^{\frac {1}{4}} x^{\frac {3}{4}}}{3} \\ y \relax (x ) = \frac {2^{\frac {3}{4}} 3^{\frac {1}{4}} x^{\frac {3}{4}}}{3} \\ y \relax (x ) = -\frac {i 2^{\frac {3}{4}} 3^{\frac {1}{4}} x^{\frac {3}{4}}}{3} \\ y \relax (x ) = \frac {i 2^{\frac {3}{4}} 3^{\frac {1}{4}} x^{\frac {3}{4}}}{3} \\ y \relax (x ) = 0 \\ y \relax (x ) = \sqrt {-4 c_{1}^{3}+2 c_{1} x} \\ y \relax (x ) = -\sqrt {-4 c_{1}^{3}+2 c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 72.887 (sec). Leaf size: 11250
DSolve[4*y[x]^2*(y'[x])^3-2*x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
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