75.19.17 problem 634

Internal problem ID [17062]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
Problem number : 634
Date solved : Monday, March 31, 2025 at 03:39:42 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y&=6 \ln \left (x +1\right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=(1+x)^3*diff(diff(y(x),x),x)+3*(1+x)^2*diff(y(x),x)+(1+x)*y(x) = 6*ln(1+x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \ln \left (x +1\right )+\ln \left (x +1\right )^{3}+c_2}{x +1} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 27

ode=(x+1)^3*D[y[x],{x,2}]+3*(x+1)^2*D[y[x],x]+(x+1)*y[x]==6*Log[x+1]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\log ^3(x+1)+c_2 \log (x+1)+c_1}{x+1} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 1)**3*Derivative(y(x), (x, 2)) + 3*(x + 1)**2*Derivative(y(x), x) + (x + 1)*y(x) - 6*log(x + 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**3*Derivative(y(x), (x, 2)) - 3*x**2*Derivative(y(x), (x, 2)) - x*y(x) - 3*x*Derivative(y(x), (x, 2)) - y(x) + 6*log(x + 1) - Derivative(y(x), (x, 2)))/(3*(x**2 + 2*x + 1)) cannot be solved by the factorable group method