29.11.26 problem 317

Internal problem ID [4917]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 317
Date solved : Sunday, March 30, 2025 at 04:13:18 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

\[ y = -\frac {\left (1+x \right ) \left (-{\mathrm e}^{x} c_1 +x \right )}{x} \]

✓ Mathematica. Time used: 0.077 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.371 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} e^{x} + \frac {C_{1} e^{x}}{x} - x - 1 \]