Internal problem ID [8122]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 542.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {16 y^{2} \left (y^{\prime }\right )^{3}+2 x y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 111
dsolve(16*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 {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3} \\ y \relax (x ) = \frac {2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3} \\ y \relax (x ) = -\frac {i 2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3} \\ y \relax (x ) = \frac {i 2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3} \\ y \relax (x ) = 0 \\ y \relax (x ) = \sqrt {16 c_{1}^{3}+2 x c_{1}} \\ y \relax (x ) = -\sqrt {16 c_{1}^{3}+2 x c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.1 (sec). Leaf size: 107
DSolve[-y[x] + 2*x*y'[x] + 16*y[x]^2*y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {c_1 \left (x+2 c_1{}^2\right )} \\ y(x)\to -\frac {\sqrt [4]{-2} x^{3/4}}{3^{3/4}} \\ y(x)\to \frac {(1-i) x^{3/4}}{\sqrt [4]{2} 3^{3/4}} \\ y(x)\to \frac {i \sqrt [4]{-2} x^{3/4}}{3^{3/4}} \\ y(x)\to \frac {\sqrt [4]{-2} x^{3/4}}{3^{3/4}} \\ \end{align*}