78.2.33 problem 10.c

Internal problem ID [20985]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 2, Second order ODEs. Problems section 2.6
Problem number : 10.c
Date solved : Thursday, October 02, 2025 at 07:01:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

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

\[ y = \frac {c_2}{x^{2}}+\frac {\ln \left (x \right ) c_1}{x^{2}}+\frac {2 x^{3}}{25} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to \frac {2 x^3}{25}+\frac {c_1}{x^2}+\frac {2 c_2 \log (x)}{x^2} \end{align*}

✓ Sympy. Time used: 0.235 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \frac {C_{1} + C_{2} \log {\left (x \right )} + \frac {2 x^{5}}{25}}{x^{2}} \]