23.3.414 problem 419

Internal problem ID [6128]
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 : 419
Date solved : Tuesday, September 30, 2025 at 02:22:01 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y = \frac {c_2 +c_1 x -\cos \left (x \right )}{\left (-1+x \right )^{2}} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \frac {-\cos (x)+c_1 (x-1)+c_2}{(x-1)^2} \end{align*}

✗ Sympy

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

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