87.14.6 problem 6

Internal problem ID [23525]
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 : 6
Date solved : Thursday, October 02, 2025 at 09:42:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+\left (x -1\right ) y^{\prime }+\left (3-12 x \right ) y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

ode:=x*diff(diff(y(x),x),x)+(x-1)*diff(y(x),x)+(3-12*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{3 x}+c_2 \,{\mathrm e}^{-4 x} \left (7 x +1\right ) \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 30

ode=x*D[y[x],{x,2}]+(x-1)*D[y[x],x]+(3-12*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{3 x}-\frac {1}{49} c_2 e^{-4 x} (7 x+1) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2)) + (3 - 12*x)*y(x) + (x - 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False