23.3.415 problem 420

Internal problem ID [6129]
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 : 420
Date solved : Tuesday, September 30, 2025 at 02:22:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 6 y-4 \left (1+x \right ) y^{\prime }+\left (1+x \right )^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=6*y(x)-4*(1+x)*diff(y(x),x)+(1+x)^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 20

ode=6*y[x] - 4*(1 + x)*D[y[x],x] + (1 + x)^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.146 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 1)**2*Derivative(y(x), (x, 2)) - (4*x + 4)*Derivative(y(x), x) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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