69.19.9 problem 626

Internal problem ID [18412]
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 : 626
Date solved : Thursday, October 02, 2025 at 03:11:35 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} \left (1+x \right )^{2} y^{\prime \prime \prime }-12 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

ode:=(1+x)^2*diff(diff(diff(y(x),x),x),x)-12*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +\frac {c_2}{\left (x +1\right )^{2}}+c_3 \left (x +1\right )^{5} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 30

ode=(x+1)^2*D[y[x],{x,3}]-12*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{5} c_1 (x+1)^5-\frac {c_2}{2 (x+1)^2}+c_3 \end{align*}

✓ Sympy. Time used: 0.183 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 1)**2*Derivative(y(x), (x, 3)) - 12*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} \left (x + 1\right )^{\frac {3}{2}} \]