73.15.54 problem 22.11 (m)

Internal problem ID [15414]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.11 (m)
Date solved : Monday, March 31, 2025 at 01:37:02 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=3 x^{2} {\mathrm e}^{5 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)-10*diff(y(x),x)+25*y(x) = 3*x^2*exp(5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{5 x} \left (c_2 +c_1 x +\frac {1}{4} x^{4}\right ) \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 27

ode=D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==3*x^2*Exp[5*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} e^{5 x} \left (x^4+4 c_2 x+4 c_1\right ) \]

✓ Sympy. Time used: 0.286 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**2*exp(5*x) + 25*y(x) - 10*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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