67.2.44 problem Problem 18(i)

Internal problem ID [13930]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 18(i)
Date solved : Monday, March 31, 2025 at 08:18:26 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 34

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

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

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 69

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

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

✗ Sympy

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

False