75.19.5 problem 622

Internal problem ID [17050]
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 : 622
Date solved : Monday, March 31, 2025 at 03:39:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x +2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }-3 y&=0 \end{align*}

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

ode:=(x+2)^2*diff(diff(y(x),x),x)+3*(x+2)*diff(y(x),x)-3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \left (x +2\right )^{4}+c_2}{\left (x +2\right )^{3}} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 20

ode=(x+2)^2*D[y[x],{x,2}]+3*(x+2)*D[y[x],x]-3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 (x+2)+\frac {c_2}{(x+2)^3} \]

✓ Sympy. Time used: 0.230 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = \frac {C_{1}}{x + 2} \]