23.1.380 problem 365

Internal problem ID [4987]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 365
Date solved : Tuesday, September 30, 2025 at 09:08:54 AM
CAS classification : [_linear]

\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=x -\left (5 x^{2}+3\right ) y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=x*(x^2+1)*diff(y(x),x) = x-(5*x^2+3)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{4}+4 c_1}{4 \left (x^{2}+1\right ) x^{3}} \]

✓ Mathematica. Time used: 0.111 (sec). Leaf size: 84

ode=x*(1+x^2)*D[y[x],x]==x-(3+5*x^2)*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x-\frac {5 K[1]^2+3}{K[1]^3+K[1]}dK[1]\right ) \left (\int _1^x\frac {\exp \left (-\int _1^{K[2]}-\frac {5 K[1]^2+3}{K[1]^3+K[1]}dK[1]\right )}{K[2]^2+1}dK[2]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.201 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x**2 + 1)*Derivative(y(x), x) - x + (5*x**2 + 3)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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