68.18.56 problem 62

Internal problem ID [17900]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 62
Date solved : Thursday, October 02, 2025 at 02:29:25 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=8 x \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 16

ode:=x^2*diff(diff(y(x),x),x)-7*x*diff(y(x),x)+15*y(x) = 8*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{5}+c_2 \,x^{3}+x \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 19

ode=x^2*D[y[x],{x,2}]-7*x*D[y[x],x]+15*y[x]==8*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x^5+c_1 x^3+x \end{align*}

✓ Sympy. Time used: 0.201 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 7*x*Derivative(y(x), x) - 8*x + 15*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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