Internal problem ID [6873]
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]]
\[ \boxed {4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 100
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 \left (x \right ) &= -\frac {2^{\frac {3}{4}} 3^{\frac {1}{4}} x^{\frac {3}{4}}}{3} \\ y \left (x \right ) &= \frac {2^{\frac {3}{4}} 3^{\frac {1}{4}} x^{\frac {3}{4}}}{3} \\ y \left (x \right ) &= -\frac {i 2^{\frac {3}{4}} 3^{\frac {1}{4}} x^{\frac {3}{4}}}{3} \\ y \left (x \right ) &= \frac {i 2^{\frac {3}{4}} 3^{\frac {1}{4}} x^{\frac {3}{4}}}{3} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \sqrt {2}\, \sqrt {c_{1} \left (-2 c_{1}^{2}+x \right )} \\ y \left (x \right ) &= -\sqrt {2}\, \sqrt {c_{1} \left (-2 c_{1}^{2}+x \right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 83.967 (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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