Internal problem ID [5333]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 9. Equations of first order and higher degree. Supplemetary problems. Page
65
Problem number: 27.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {y-2 y^{\prime } x -y^{2} {y^{\prime }}^{3}=0} \]
✓ Solution by Maple
Time used: 0.485 (sec). Leaf size: 107
dsolve(y(x)=2*x*diff(y(x),x)+y(x)^2*diff(y(x),x)^3,y(x), singsol=all)
\begin{align*} y = -\frac {2 \,2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3} y = \frac {2 \,2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3} y = -\frac {2 i 2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3} y = \frac {2 i 2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3} y = 0 y = \sqrt {c_{1}^{3}+2 c_{1} x} y = -\sqrt {c_{1}^{3}+2 c_{1} x} \end{align*}
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 119
DSolve[y[x]==2*x*y'[x]+y[x]^2*y'[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2 c_1 x+c_1{}^3} y(x)\to \sqrt {2 c_1 x+c_1{}^3} y(x)\to (-1-i) \left (\frac {2}{3}\right )^{3/4} x^{3/4} y(x)\to (1-i) \left (\frac {2}{3}\right )^{3/4} x^{3/4} y(x)\to (-1+i) \left (\frac {2}{3}\right )^{3/4} x^{3/4} y(x)\to (1+i) \left (\frac {2}{3}\right )^{3/4} x^{3/4} \end{align*}