56.3.16 problem 16

Internal problem ID [8874]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 16
Date solved : Sunday, March 30, 2025 at 01:45:19 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 22

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

\[ y = \frac {3 c_2 \,x^{4}+3 c_1 -x}{3 x^{2}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 25

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

\[ y(x)\to c_2 x^2+\frac {c_1}{x^2}-\frac {1}{3 x} \]

✓ Sympy. Time used: 0.235 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \frac {C_{1} + C_{2} x^{4} - \frac {x}{3}}{x^{2}} \]