81.1.21 problem 2-19

Internal problem ID [21466]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-19
Date solved : Thursday, October 02, 2025 at 07:39:00 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 57

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

\begin{align*} y &= \left (2 x^{2}+c_1 \right )^{{1}/{4}} \\ y &= -\left (2 x^{2}+c_1 \right )^{{1}/{4}} \\ y &= -i \left (2 x^{2}+c_1 \right )^{{1}/{4}} \\ y &= i \left (2 x^{2}+c_1 \right )^{{1}/{4}} \\ \end{align*}

✓ Mathematica. Time used: 0.125 (sec). Leaf size: 96

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

\begin{align*} y(x)&\to -\sqrt [4]{2} \sqrt [4]{x^2+2 c_1}\\ y(x)&\to -i \sqrt [4]{2} \sqrt [4]{x^2+2 c_1}\\ y(x)&\to i \sqrt [4]{2} \sqrt [4]{x^2+2 c_1}\\ y(x)&\to \sqrt [4]{2} \sqrt [4]{x^2+2 c_1} \end{align*}

✓ Sympy. Time used: 0.408 (sec). Leaf size: 54

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

\[ \left [ y{\left (x \right )} = - i \sqrt [4]{C_{1} + 2 x^{2}}, \ y{\left (x \right )} = i \sqrt [4]{C_{1} + 2 x^{2}}, \ y{\left (x \right )} = - \sqrt [4]{C_{1} + 2 x^{2}}, \ y{\left (x \right )} = \sqrt [4]{C_{1} + 2 x^{2}}\right ] \]