44.5.64 problem 54

Internal problem ID [7126]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 54
Date solved : Sunday, March 30, 2025 at 11:47:51 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x \arctan \left (x \right )}{y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Maple. Time used: 0.098 (sec). Leaf size: 19

ode:=diff(y(x),x) = x*arctan(x)/y(x); 
ic:=y(0) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \sqrt {\arctan \left (x \right ) x^{2}+\arctan \left (x \right )-x +9} \]

✓ Mathematica. Time used: 0.144 (sec). Leaf size: 22

ode=D[y[x],x]==x*ArcTan[x]/y[x]; 
ic={y[0]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sqrt {x^2 \arctan (x)+\arctan (x)-x+9} \]

✓ Sympy. Time used: 0.433 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \sqrt {x^{2} \operatorname {atan}{\left (x \right )} - x + \operatorname {atan}{\left (x \right )} + 9} \]