64.13.24 problem 24

Internal problem ID [13483]
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 : 24
Date solved : Monday, March 31, 2025 at 07:59:17 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=-6 x^{3}+4 x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=4\\ y^{\prime }\left (2\right )&=-1 \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 23

ode:=x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+4*y(x) = -6*x^3+4*x^2; 
ic:=y(2) = 4, D(y)(2) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {23}{24} x^{4}+3 x^{3}-2 x^{2}+\frac {5}{3} x \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 28

ode=x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+4*y[x]==4*x^2-6*x^3; 
ic={y[2]==4,Derivative[1][y][2]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {23 x^4}{24}+3 x^3-2 x^2+\frac {5 x}{3} \]

✓ Sympy. Time used: 0.353 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x**3 + x**2*Derivative(y(x), (x, 2)) - 4*x**2 - 4*x*Derivative(y(x), x) + 4*y(x),0) 
ics = {y(2): 4, Subs(Derivative(y(x), x), x, 2): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \left (- \frac {23 x^{3}}{24} + 3 x^{2} - 2 x + \frac {5}{3}\right ) \]