23.1.289 problem 282

Internal problem ID [4896]
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 : 282
Date solved : Tuesday, September 30, 2025 at 08:55:55 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

\[ y = \sqrt {x -1}\, \sqrt {x +1}\, c_1 +5 x \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to 5 x+c_1 \sqrt {x^2-1} \end{align*}

✓ Sympy. Time used: 1.595 (sec). Leaf size: 51

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

\[ y{\left (x \right )} = \begin {cases} C_{1} \sqrt {x^{2} - 1} + 5 x & \text {for}\: x > 1 \vee x < -1 \\C_{1} \sqrt {x^{2} - 1} - \frac {5 i x \sqrt {x^{2} - 1}}{\sqrt {1 - x^{2}}} & \text {otherwise} \end {cases} \]