Internal problem ID [4300]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 36
Problem number: 1085.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 167
dsolve(y(x)^4*diff(y(x),x)^3-6*x*diff(y(x),x)+2*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {x \left (-1-i \sqrt {3}\right )} \\ y \left (x \right ) &= \sqrt {\left (-1+i \sqrt {3}\right ) x} \\ y \left (x \right ) &= -\sqrt {-\left (1+i \sqrt {3}\right ) x} \\ y \left (x \right ) &= -\sqrt {\left (-1+i \sqrt {3}\right ) x} \\ y \left (x \right ) &= \sqrt {2}\, \sqrt {x} \\ y \left (x \right ) &= -\sqrt {2}\, \sqrt {x} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {2^{\frac {2}{3}} \left (-c_{1}^{3}+6 c_{1} x \right )^{\frac {1}{3}}}{2} \\ y \left (x \right ) &= -\frac {2^{\frac {2}{3}} \left (-c_{1}^{3}+6 c_{1} x \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{4} \\ y \left (x \right ) &= \frac {2^{\frac {2}{3}} \left (-c_{1}^{3}+6 c_{1} x \right )^{\frac {1}{3}} \left (-1+i \sqrt {3}\right )}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 81.226 (sec). Leaf size: 22649
DSolve[y[x]^4 (y'[x])^3 -6 x y'[x] +2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Too large to display