6.20.2 problem section 9.4, problem 8

Internal problem ID [2223]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.4. Variation of Parameters for Higher Order Equations. Page 503
Problem number : section 9.4, problem 8
Date solved : Tuesday, September 30, 2025 at 05:25:11 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 x y^{\prime }+2 y&=30 x^{2} \end{align*}

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

ode:=4*x^3*diff(diff(diff(y(x),x),x),x)+4*x^2*diff(diff(y(x),x),x)-5*x*diff(y(x),x)+2*y(x) = 30*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (c_1 +2 \ln \left (x \right )-\frac {32}{15}\right ) x^{{5}/{2}}+c_3 x +c_2}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 38

ode=4*x^3*D[y[x],{x,3}]+4*x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+2*y[x]==30*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 x^2 \log (x)+\frac {\left (-\frac {32}{15}+c_3\right ) x^{5/2}+c_2 x+c_1}{\sqrt {x}} \end{align*}

✓ Sympy. Time used: 0.204 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**3*Derivative(y(x), (x, 3)) + 4*x**2*Derivative(y(x), (x, 2)) - 30*x**2 - 5*x*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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