87.13.24 problem 28

Internal problem ID [23507]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 100
Problem number : 28
Date solved : Thursday, October 02, 2025 at 09:42:34 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{5} y^{\left (5\right )}-2 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=x^5*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-2*x^3*diff(diff(diff(y(x),x),x),x)+4*x^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \left (c_3 \,x^{3}+c_5 \right ) \ln \left (x \right )+c_2 \,x^{4}+c_4 x +c_1 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 50

ode=x^5*D[y[x],{x,5}]-2*x^3*D[y[x],{x,3}]+4*x^2*D[y[x],{x,2}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{144} (12 c_2-7 c_3) x^4+\left (\frac {c_3 x^4}{12}+c_1 x\right ) \log (x)+(c_5-c_1) x+c_4 \end{align*}

✓ Sympy. Time used: 0.084 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**5*Derivative(y(x), (x, 5)) - 2*x**3*Derivative(y(x), (x, 3)) + 4*x**2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{4} + C_{4} x \log {\left (x \right )} + C_{5} x^{4} \log {\left (x \right )} \]