4.2.16 problem 16

Internal problem ID [1144]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 16
Date solved : Tuesday, September 30, 2025 at 04:23:44 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x \left (x^{2}+1\right )}{4 y^{3}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-\frac {\sqrt {2}}{2} \\ \end{align*}

✓ Maple. Time used: 0.118 (sec). Leaf size: 15

ode:=diff(y(x),x) = 1/4*x*(x^2+1)/y(x)^3; 
ic:=[y(0) = -1/2*2^(1/2)]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {\sqrt {2 x^{2}+2}}{2} \]

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 23

ode=D[y[x],x] == 1/4*x*(x^2+1)/y[x]^3; 
ic=y[0]==-(1/Sqrt[2]); 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\sqrt [4]{\left (x^2+1\right )^2}}{\sqrt {2}} \end{align*}

✓ Sympy. Time used: 1.461 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(x**2 + 1)/(4*y(x)**3) + Derivative(y(x), x),0) 
ics = {y(0): -sqrt(2)/2} 
dsolve(ode,func=y(x),ics=ics)
 

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