29.36.14 problem 1080

Internal problem ID [5641]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1080
Date solved : Sunday, March 30, 2025 at 09:40:47 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} 16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.294 (sec). Leaf size: 102

ode:=16*y(x)^2*diff(y(x),x)^3+2*x*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {\left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= \frac {\left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= -\frac {i \left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= \frac {i \left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= 0 \\ y &= \sqrt {2}\, \sqrt {c_1 \left (8 c_1^{2}+x \right )} \\ y &= -\sqrt {2}\, \sqrt {c_1 \left (8 c_1^{2}+x \right )} \\ \end{align*}

✓ Mathematica. Time used: 0.119 (sec). Leaf size: 107

ode=16 y[x]^2 (D[y[x],x])^3 +2 x D[y[x],x] -y[x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*Derivative(y(x), x) + 16*y(x)**2*Derivative(y(x), x)**3 - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

IndexError : list index out of range