71.4.7 problem 7

Internal problem ID [14300]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 7
Date solved : Wednesday, March 05, 2025 at 10:44:26 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x}{y^{2}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 63

ode:=diff(y(x),x) = x/y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\left (12 x^{2}+8 c_{1} \right )^{{1}/{3}}}{2} \\ y &= -\frac {\left (12 x^{2}+8 c_{1} \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4} \\ y &= \frac {\left (12 x^{2}+8 c_{1} \right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.188 (sec). Leaf size: 79

ode=D[y[x],x]==x/y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\sqrt [3]{-\frac {3}{2}} \sqrt [3]{x^2+2 c_1} \\ y(x)\to \sqrt [3]{\frac {3}{2}} \sqrt [3]{x^2+2 c_1} \\ y(x)\to (-1)^{2/3} \sqrt [3]{\frac {3}{2}} \sqrt [3]{x^2+2 c_1} \\ \end{align*}

✓ Sympy. Time used: 0.771 (sec). Leaf size: 63

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

\[ \left [ y{\left (x \right )} = \sqrt [3]{C_{1} + \frac {3 x^{2}}{2}}, \ y{\left (x \right )} = \frac {\left (-1 - \sqrt {3} i\right ) \sqrt [3]{C_{1} + \frac {3 x^{2}}{2}}}{2}, \ y{\left (x \right )} = \frac {\left (-1 + \sqrt {3} i\right ) \sqrt [3]{C_{1} + \frac {3 x^{2}}{2}}}{2}\right ] \]