76.10.5 problem Ex. 5

Internal problem ID [20045]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 27
Problem number : Ex. 5
Date solved : Thursday, October 02, 2025 at 05:16:05 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=(x^2+1)*diff(y(x),x)+2*x*y(x) = 4*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {4 x^{3}+3 c_1}{3 x^{2}+3} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {4 x^3+3 c_1}{3 x^2+3} \end{align*}

✓ Sympy. Time used: 0.152 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \frac {C_{1} + \frac {4 x^{3}}{3}}{x^{2} + 1} \]