51.1.58 problem 58

Internal problem ID [10328]
Book : First order enumerated odes
Section : section 1
Problem number : 58
Date solved : Tuesday, September 30, 2025 at 07:19:32 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} {y^{\prime }}^{4}&=\frac {1}{x y^{3}} \end{align*}

✓ Maple. Time used: 0.050 (sec). Leaf size: 123

ode:=diff(y(x),x)^4 = 1/x/y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} -\frac {c_1 \,x^{{9}/{4}}-3 \left (x^{3} y\right )^{{3}/{4}} y+7 x^{3}}{x^{{9}/{4}}} &= 0 \\ \frac {-7 x^{3}+3 i \left (x^{3} y\right )^{{3}/{4}} y-c_1 \,x^{{9}/{4}}}{x^{{9}/{4}}} &= 0 \\ \frac {7 x^{3}+3 i \left (x^{3} y\right )^{{3}/{4}} y-c_1 \,x^{{9}/{4}}}{x^{{9}/{4}}} &= 0 \\ \frac {7 x^{3}+3 \left (x^{3} y\right )^{{3}/{4}} y-c_1 \,x^{{9}/{4}}}{x^{{9}/{4}}} &= 0 \\ \end{align*}

✓ Mathematica. Time used: 6.607 (sec). Leaf size: 129

ode=(D[y[x],x])^4==1/(x*y[x]^3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\left (-\frac {28 x^{3/4}}{3}+7 c_1\right ){}^{4/7}}{2 \sqrt [7]{2}}\\ y(x)&\to \frac {\left (7 c_1-\frac {28}{3} i x^{3/4}\right ){}^{4/7}}{2 \sqrt [7]{2}}\\ y(x)&\to \frac {\left (\frac {28}{3} i x^{3/4}+7 c_1\right ){}^{4/7}}{2 \sqrt [7]{2}}\\ y(x)&\to \frac {\left (\frac {28 x^{3/4}}{3}+7 c_1\right ){}^{4/7}}{2 \sqrt [7]{2}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)**4 - 1/(x*y(x)**3),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out