Internal problem ID [4297]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 36
Problem number: 1080.
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: 0.266 (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 \left (x \right ) = -\frac {2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3} y \left (x \right ) = \frac {2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3} y \left (x \right ) = -\frac {i 2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3} y \left (x \right ) = \frac {i 2^{\frac {1}{4}} 3^{\frac {1}{4}} \left (-x^{3}\right )^{\frac {1}{4}}}{3} y \left (x \right ) = 0 y \left (x \right ) = \sqrt {16 c_{1}^{3}+2 c_{1} x} y \left (x \right ) = -\sqrt {16 c_{1}^{3}+2 c_{1} x} \end{align*}
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 107
DSolve[16 y[x]^2 (y'[x])^3 +2 x y'[x] -y[x]==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*}