73.10.9 problem 15.2 (i)

Internal problem ID [15233]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.2 (i)
Date solved : Monday, March 31, 2025 at 01:31:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 13

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

\[ y = 4 x^{2}+4 x \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 11

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

\[ y(x)\to 4 x (x+1) \]

✗ Sympy

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

ValueError : Couldnt solve for initial conditions