67.4.26 problem 5.3 (f)

Internal problem ID [16395]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.3 (f)
Date solved : Thursday, October 02, 2025 at 01:27:37 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (2\right )&=8 \\ \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 21

ode:=(x^2+1)*diff(y(x),x) = x*(3+3*x^2-y(x)); 
ic:=[y(2) = 8]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x^{2}+1+\frac {3 \sqrt {5}}{\sqrt {x^{2}+1}} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 26

ode=(1+x^2)*D[y[x],x]==x*(3+3*x^2-y[x]); 
ic={y[2]==8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2+\frac {3 \sqrt {5}}{\sqrt {x^2+1}}+1 \end{align*}

✓ Sympy. Time used: 0.256 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(3*x**2 - y(x) + 3) + (x**2 + 1)*Derivative(y(x), x),0) 
ics = {y(2): 8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} + 1 + \frac {3 \sqrt {5}}{\sqrt {x^{2} + 1}} \]