76.1.1 problem 1

Internal problem ID [17229]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 1
Date solved : Monday, March 31, 2025 at 03:45:09 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 33

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

\begin{align*} y &= -\frac {\sqrt {10 x^{5}+25 c_1}}{5} \\ y &= \frac {\sqrt {10 x^{5}+25 c_1}}{5} \\ \end{align*}

✓ Mathematica. Time used: 0.103 (sec). Leaf size: 50

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

\begin{align*} y(x)\to -\sqrt {\frac {2}{5}} \sqrt {x^5+5 c_1} \\ y(x)\to \sqrt {\frac {2}{5}} \sqrt {x^5+5 c_1} \\ \end{align*}

✓ Sympy. Time used: 0.244 (sec). Leaf size: 29

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

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {C_{1} + 10 x^{5}}}{5}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} + 10 x^{5}}}{5}\right ] \]