23.1.306 problem 296

Internal problem ID [4913]
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 : 296
Date solved : Tuesday, September 30, 2025 at 08:56:26 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to \frac {-a x \left (x^2-3\right )+3 c_1}{3 \left (x^2-1\right )^2} \end{align*}

✓ Sympy. Time used: 0.200 (sec). Leaf size: 24

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

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