64.13.26 problem 26

Internal problem ID [13485]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 26
Date solved : Monday, March 31, 2025 at 07:59:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=2 x^{3} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 15

ode:=x^2*diff(diff(y(x),x),x)-5*x*diff(y(x),x)+8*y(x) = 2*x^3; 
ic:=y(2) = 0, D(y)(2) = -8; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -2 x^{3}+4 x^{2} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 13

ode=x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+8*y[x]==2*x^3; 
ic={y[2]==0,Derivative[1][y][2]==-8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -2 (x-2) x^2 \]

✓ Sympy. Time used: 0.342 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x**3 + x**2*Derivative(y(x), (x, 2)) - 5*x*Derivative(y(x), x) + 8*y(x),0) 
ics = {y(2): 0, Subs(Derivative(y(x), x), x, 2): -8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} \left (4 - 2 x\right ) \]