40.13.10 problem 30

Internal problem ID [6764]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number : 30
Date solved : Wednesday, March 05, 2025 at 02:43:11 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y&=\frac {1+x}{x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=x^4*diff(diff(y(x),x),x)+2*x^3*diff(y(x),x)+y(x) = (1+x)/x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.073 (sec). Leaf size: 25

ode=x^4*D[y[x],{x,2}]+2*x^3*D[y[x],x]+y[x]==(1+x)/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{x}+c_1 \cos \left (\frac {1}{x}\right )-c_2 \sin \left (\frac {1}{x}\right )+1 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 2)) + 2*x**3*Derivative(y(x), x) + y(x) - (x + 1)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**5*Derivative(y(x), (x, 2)) + x*(1 - y(x)) + 1)/(2*x**4) cannot be solved by the factorable group method