Internal problem ID [8877]
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]]
\[ \boxed {16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 104
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 \left (x \right ) &= -\frac {\left (-x^{3}\right )^{\frac {1}{4}} 6^{\frac {1}{4}}}{3} \\ y \left (x \right ) &= \frac {\left (-x^{3}\right )^{\frac {1}{4}} 6^{\frac {1}{4}}}{3} \\ y \left (x \right ) &= -\frac {i \left (-x^{3}\right )^{\frac {1}{4}} 6^{\frac {1}{4}}}{3} \\ y \left (x \right ) &= \frac {i \left (-x^{3}\right )^{\frac {1}{4}} 6^{\frac {1}{4}}}{3} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \sqrt {2}\, \sqrt {c_{1} \left (8 c_{1}^{2}+x \right )} \\ y \left (x \right ) &= -\sqrt {2}\, \sqrt {c_{1} \left (8 c_{1}^{2}+x \right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.115 (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*}