49.13.6 problem 1(f)

Internal problem ID [7682]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 3. Linear equations with variable coefficients. Page 121
Problem number : 1(f)
Date solved : Sunday, March 30, 2025 at 12:18:51 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=x \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

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

\[ y = -{\mathrm e}^{x^{2}} c_2 +x \left (c_2 \sqrt {\pi }\, \operatorname {erfi}\left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 43

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

\[ y(x)\to -\sqrt {\pi } c_2 \sqrt {x^2} \text {erfi}\left (\sqrt {x^2}\right )+c_2 e^{x^2}+2 c_1 x \]

✗ Sympy

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

False