23.3.441 problem 446

Internal problem ID [6155]
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 : 446
Date solved : Tuesday, September 30, 2025 at 02:23:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = c_2 \sqrt {1+x}+c_1 x +c_1 \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.140 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = C_{1} \left (x + 1\right )^{\frac {3}{4}} \]