59.1.22 problem 22

Internal problem ID [9194]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 22
Date solved : Wednesday, March 05, 2025 at 07:37:39 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y^{\prime \prime }+x y^{\prime }+3 y&=0 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 32

ode:=2*diff(diff(y(x),x),x)+x*diff(y(x),x)+3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x^{2}-2\right ) \left (c_{1} \operatorname {erfi}\left (\frac {x}{2}\right ) \sqrt {\pi }+c_{2} \right ) {\mathrm e}^{-\frac {x^{2}}{4}}-2 c_{1} x \]

✓ Mathematica. Time used: 0.408 (sec). Leaf size: 52

ode=2*D[y[x],{x,2}]+x*D[y[x],x]+3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-\frac {x^2}{4}} \left (x^2-2\right ) \left (c_2 \int _1^x\frac {e^{\frac {K[1]^2}{4}}}{\left (K[1]^2-2\right )^2}dK[1]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + 3*y(x) + 2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False