56.3.15 problem 15

Internal problem ID [8873]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 15
Date solved : Wednesday, March 05, 2025 at 07:00:17 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=1 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 24

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

\[ y = \frac {16 c_{2} x^{4}-4 \ln \left (x \right )+16 c_{1} -1}{16 x^{2}} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 29

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

\[ y(x)\to \frac {16 c_2 x^4-4 \log (x)-1+16 c_1}{16 x^2} \]

✓ Sympy. Time used: 0.456 (sec). Leaf size: 17

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) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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