67.2.57 problem Problem 20(d)

Internal problem ID [13943]
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 20(d)
Date solved : Monday, March 31, 2025 at 08:19:46 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 24

ode:=(x^2-x)*diff(diff(y(x),x),x)+(2*x^2+4*x-3)*diff(y(x),x)+8*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.347 (sec). Leaf size: 112

ode=(x^2-x)*D[y[x],{x,2}]+(2*x^2+4*x-3)*D[y[x],x]+8*x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x\left (-\frac {1}{2 K[1]}+1+\frac {1}{2-2 K[1]}\right )dK[1]-\frac {1}{2} \int _1^x\left (\frac {3}{K[2]}+2+\frac {3}{K[2]-1}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {2 K[1]^2-4 K[1]+1}{2 (K[1]-1) K[1]}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*x*y(x) + (x**2 - x)*Derivative(y(x), (x, 2)) + (2*x**2 + 4*x - 3)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False