73.14.18 problem 21.15 (i)

Internal problem ID [15357]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 21. Nonhomogeneous equations in general. Additional exercises page 391
Problem number : 21.15 (i)
Date solved : Monday, March 31, 2025 at 01:35:19 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 20

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

\[ y = c_2 \,x^{5}+c_1 \,x^{3}+\frac {1}{3} x^{2} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 25

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

\[ y(x)\to c_2 x^5+c_1 x^3+\frac {x^2}{3} \]

✓ Sympy. Time used: 0.355 (sec). Leaf size: 17

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

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