68.15.25 problem 25

Internal problem ID [17751]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 25
Date solved : Thursday, October 02, 2025 at 02:27:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=2 x \end{align*}

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

ode:=x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-6*y(x) = 2*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,x^{2}+\frac {c_1}{x^{3}}-\frac {x}{2} \]

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

ode=x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-6*y[x]==2*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.146 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 2*x*Derivative(y(x), x) - 2*x - 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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