8.11.35 problem 58

Internal problem ID [903]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 58
Date solved : Tuesday, March 04, 2025 at 12:00:18 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 19

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

\[ y = x^{2} \left (x \ln \left (x \right )+\left (c_1 -1\right ) x +c_2 \right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 22

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

\[ y(x)\to x^2 (x \log (x)+(-1+c_2) x+c_1) \]

✓ Sympy. Time used: 0.231 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = x^{2} \left (C_{1} + C_{2} x + x \log {\left (x \right )}\right ) \]