87.14.17 problem 17

Internal problem ID [23536]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 109
Problem number : 17
Date solved : Thursday, October 02, 2025 at 09:42:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 y-2 x y^{\prime }+y^{\prime \prime }&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=8 x^{3}-12 x \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-2*x*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \left (-\frac {2}{3} x^{3}+x \right )+c_2 \operatorname {hypergeom}\left (\left [-\frac {3}{2}\right ], \left [\frac {1}{2}\right ], x^{2}\right ) \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 71

ode=D[y[x],{x,2}]-2*x*D[y[x],x]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \sqrt {\pi } c_2 \sqrt {x^2} \left (2 x^2-3\right ) \text {erfi}\left (\sqrt {x^2}\right )+8 c_1 x^3-c_2 e^{x^2} x^2+c_2 e^{x^2}-12 c_1 x \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*Derivative(y(x), x) + 6*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False