73.14.21 problem 21.15 (c)

Internal problem ID [15352]
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 (c)
Date solved : Thursday, March 13, 2025 at 05:55:46 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=4 x^{2}+2 x +3 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 24

ode:=x^2*diff(diff(y(x),x),x)-7*x*diff(y(x),x)+15*y(x) = 4*x^2+2*x+3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{2} x^{5}+c_{1} x^{3}+\frac {1}{5}+\frac {4}{3} x^{2}+\frac {1}{4} x \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 33

ode=x^2*D[y[x],{x,2}]-7*x*D[y[x],x]+15*y[x]==4*x^2+2*x+3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 x^5+c_1 x^3+\frac {4 x^2}{3}+\frac {x}{4}+\frac {1}{5} \]

✓ Sympy. Time used: 0.396 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 4*x**2 - 7*x*Derivative(y(x), x) - 2*x + 15*y(x) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x^{3} + C_{2} x^{5} + \frac {4 x^{2}}{3} + \frac {x}{4} + \frac {1}{5} \]