23.3.368 problem 372

Internal problem ID [6082]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 372
Date solved : Tuesday, September 30, 2025 at 02:21:11 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} 2 y+4 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=-2 x +2 \cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 31

ode:=2*y(x)+4*x*diff(y(x),x)+(x^2+1)*diff(diff(y(x),x),x) = -2*x+2*cos(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-x^{3}+3 c_1 x -6 \cos \left (x \right )+3 c_2}{3 x^{2}+3} \]

✓ Mathematica. Time used: 0.059 (sec). Leaf size: 33

ode=2*y[x] + 4*x*D[y[x],x] + (1 + x^2)*D[y[x],{x,2}] == 2*(-x + Cos[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x^3+6 \cos (x)-3 c_2 x-3 c_1}{3 x^2+3} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*Derivative(y(x), x) + 2*x + (x**2 + 1)*Derivative(y(x), (x, 2)) + 2*y(x) - 2*cos(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x*(x*Derivative(y(x), (x, 2)) + 2) - 2*y