29.11.2 problem 293

Internal problem ID [4893]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 293
Date solved : Sunday, March 30, 2025 at 04:09:21 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: 0.036 (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]
 

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

✓ Sympy. Time used: 0.334 (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)
 

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