29.12.34 problem 353

Internal problem ID [4953]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 353
Date solved : Tuesday, March 04, 2025 at 07:34:42 PM
CAS classification : [_linear]

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

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

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

\[ y \left (x \right ) = \frac {\left (a \,\operatorname {arcsinh}\left (x \right )+c_{1} \right ) x}{\sqrt {x^{2}+1}} \]

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 2.619 (sec). Leaf size: 19

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

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