78.2.32 problem 10.b

Internal problem ID [20984]
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.b
Date solved : Thursday, October 02, 2025 at 07:01:01 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

\[ y = \frac {c_1}{x}+\frac {c_2}{\sqrt {x}}+\frac {x^{2}}{15}+\frac {x}{6} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to \frac {x^2}{15}+\frac {x}{6}+\frac {c_2}{\sqrt {x}}+\frac {c_1}{x} \end{align*}

✓ Sympy. Time used: 0.168 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \frac {C_{1}}{x} + \frac {C_{2}}{\sqrt {x}} + \frac {x^{2}}{15} + \frac {x}{6} \]