29.13.1 problem 355

Internal problem ID [4955]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 355
Date solved : Sunday, March 30, 2025 at 04:21:06 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 2.659 (sec). Leaf size: 15

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

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