75.6.2 problem 2

Internal problem ID [19970]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter V. Homogeneous linear differential equations. Exact equations. Exercises at page 69
Problem number : 2
Date solved : Thursday, October 02, 2025 at 05:04:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y&=x \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 18

ode:=x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)-8*y(x) = x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2}{x^{4}}+c_1 \,x^{2}-\frac {x}{5} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 23

ode=x^2*D[y[x],{x,2}]+3*x*D[y[x],x]-8*y[x]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{x^4}+c_2 x^2-\frac {x}{5} \end{align*}

✓ Sympy. Time used: 0.149 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 3*x*Derivative(y(x), x) - x - 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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