50.2.13 problem 2(c)

Internal problem ID [7819]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 2(c)
Date solved : Wednesday, March 05, 2025 at 05:07:03 AM
CAS classification : [_separable]

\begin{align*} \frac {y^{\prime }}{x^{2}+1}&=\frac {x}{y} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 20

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

\[ y = \frac {\sqrt {2 x^{4}+4 x^{2}+30}}{2} \]

✓ Mathematica. Time used: 0.109 (sec). Leaf size: 25

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

\[ y(x)\to \frac {\sqrt {x^4+2 x^2+15}}{\sqrt {2}} \]

✓ Sympy. Time used: 0.486 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \frac {\sqrt {2 x^{4} + 4 x^{2} + 30}}{2} \]